sequences.py

EXAMPLE_LOG_AS_INTS = [
    (1, 2, 3, 4),
    (1, 3, 2, 4),
]
"""An example XES trace converted to integers."""

FIB = [
    1,
    1,
    2,
    3,
    5,
    8,
    13,
    21,
    34,
    55,
    89,
    144,
    233,
    377,
    610,
    987,
    1597,
    2584,
    4181,
    6765,
    10946,
    17711,
    28657,
    46368,
    75025,
    121393,
    196418,
    317811,
    514229,
    832040,
    1346269,
    2178309,
    3524578,
    5702887,
    9227465,
    14930352,
    24157817,
    39088169,
    63245986,
    102334155,
    165580141,
    267914296,
    433494437,
    701408733,
    1134903170,
    1836311903,
    2971215073,
    4807526976,
    7778742049,
    12586269025,
    20365011074,
    32951280099,
    53316291173,
    86267571272,
    139583862445,
    225851433717,
    365435296162,
    591286729879,
    956722026041,
    1548008755920,
    2504730781961,
    4052739537881,
    6557470319842,
    10610209857723,
    17167680177565,
    27777890035288,
    44945570212853,
    72723460248141,
    117669030460994,
    190392490709135,
    308061521170129,
    498454011879264,
    806515533049393,
    1304969544928657,
    2111485077978050,
    3416454622906707,
    5527939700884757,
    8944394323791464,
    14472334024676221,
    23416728348467685,
    37889062373143906,
    61305790721611591,
    99194853094755497,
    160500643816367088,
    259695496911122585,
    420196140727489673,
    679891637638612258,
    1100087778366101931,
    1779979416004714189,
    2880067194370816120,
    4660046610375530309,
    7540113804746346429,
    12200160415121876738,
    19740274219868223167,
    31940434634990099905,
    51680708854858323072,
    83621143489848422977,
    135301852344706746049,
    218922995834555169026,
    354224848179261915075,
]
"""First 100 digits in the fibonacci sequence."""

PASCAL = [
    1,
    1,
    1,
    1,
    2,
    1,
    1,
    3,
    3,
    1,
    1,
    4,
    6,
    4,
    1,
    1,
    5,
    10,
    10,
    5,
    1,
    1,
    6,
    15,
    20,
    15,
    6,
    1,
    1,
    7,
    21,
    35,
    35,
    21,
    7,
    1,
    1,
    8,
    28,
    56,
    70,
    56,
    28,
    8,
    1,
    1,
    9,
    36,
    84,
    126,
    126,
    84,
    36,
    9,
    1,
    1,
    10,
    45,
    120,
    210,
    252,
    210,
    120,
    45,
    10,
    1,
    1,
    11,
    55,
    165,
    330,
    462,
    462,
    330,
    165,
    55,
    11,
    1,
    1,
    12,
    66,
    220,
    495,
    792,
    924,
    792,
    495,
    220,
    66,
    12,
    1,
    1,
    13,
    78,
    286,
    715,
    1287,
    1716,
    1716,
    1287,
]
"""First 100 digits in the sequence given by the triangle of pascal."""

CATALAN = [
    1,
    1,
    2,
    5,
    14,
    42,
    132,
    429,
    1430,
    4862,
    16796,
    58786,
    208012,
    742900,
    2674440,
    9694845,
    35357670,
    129644790,
    477638700,
    1767263190,
    6564120420,
    24466267020,
    91482563640,
    343059613650,
    1289904147324,
    4861946401452,
    18367353072152,
    69533550916004,
    263747951750360,
    1002242216651368,
    3814986502092304,
    14544636039226909,
    55534064877048198,
    212336130412243110,
    812944042149730764,
    3116285494907301262,
    11959798385860453492,
    45950804324621742364,
    176733862787006701400,
    680425371729975800390,
    2622127042276492108820,
    10113918591637898134020,
    39044429911904443959240,
    150853479205085351660700,
    583300119592996693088040,
    2257117854077248073253720,
    8740328711533173390046320,
    33868773757191046886429490,
    131327898242169365477991900,
    509552245179617138054608572,
    1978261657756160653623774456,
    7684785670514316385230816156,
    29869166945772625950142417512,
    116157871455782434250553845880,
    451959718027953471447609509424,
    1759414616608818870992479875972,
    6852456927844873497549658464312,
    26700952856774851904245220912664,
    104088460289122304033498318812080,
    405944995127576985730643443367112,
    1583850964596120042686772779038896,
    6182127958584855650487080847216336,
    24139737743045626825711458546273312,
    94295850558771979787935384946380125,
    368479169875816659479009042713546950,
    1440418573150919668872489894243865350,
    5632681584560312734993915705849145100,
    22033725021956517463358552614056949950,
    86218923998960285726185640663701108500,
    337485502510215975556783793455058624700,
    1321422108420282270489942177190229544600,
    5175569924646105559418940193995065716350,
    20276890389709399862928998568254641025700,
    79463489365077377841208237632349268884500,
    311496878311103321137536291518809134027240,
    1221395654430378811828760722007962130791020,
    4790408930363303911328386208394864461024520,
    18793142726809884575211361279087545193250040,
    73745243611532458459690151854647329239335600,
    289450081175264899454283846029490767264392230,
    1136359577947336271931632877004667456667613940,
    4462290049988320482463241297506133183499654740,
    17526585015616776834735140517915655636396234280,
    68854441132780194707888052034668647142985206100,
    270557451039395118028642463289168566420671280440,
    1063353702922273835973036658043476458723103404520,
    4180080073556524734514695828170907458428751314320,
    16435314834665426797069144960762886143367590394940,
    64633260585762914370496637486146181462681535261000,
    254224158304000796523953440778841647086547372026600,
    1000134600800354781929399250536541864362461089950800,
    3935312233584004685417853572763349509774031680023800,
    15487357822491889407128326963778343232013931127835600,
    60960876535340415751462563580829648891969728907438000,
    239993345518077005168915776623476723006280827488229600,
    944973797977428207852605870454939596837230758234904050,
    3721443204405954385563870541379246659709506697378694300,
    14657929356129575437016877846657032761712954950899755100,
    57743358069601357782187700608042856334020731624756611000,
    227508830794229349661819540395688853956041682601541047340,
    896519947090131496687170070074100632420837521538745909320,
]
"""First 100 catalan numbers."""

RECAMAN = [
    0,
    1,
    3,
    6,
    2,
    7,
    13,
    20,
    12,
    21,
    11,
    22,
    10,
    23,
    9,
    24,
    8,
    25,
    43,
    62,
    42,
    63,
    41,
    18,
    42,
    17,
    43,
    16,
    44,
    15,
    45,
    14,
    46,
    79,
    113,
    78,
    114,
    77,
    39,
    78,
    38,
    79,
    37,
    80,
    36,
    81,
    35,
    82,
    34,
    83,
    33,
    84,
    32,
    85,
    31,
    86,
    30,
    87,
    29,
    88,
    28,
    89,
    27,
    90,
    26,
    91,
    157,
    224,
    156,
    225,
    155,
    226,
    154,
    227,
    153,
    228,
    152,
    75,
    153,
    74,
    154,
    73,
    155,
    72,
    156,
    71,
    157,
    70,
    158,
    69,
    159,
    68,
    160,
    67,
    161,
    66,
    162,
    65,
    163,
    64,
]
"""First 100 digits in the recaman sequence."""


UP = [
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    15,
    16,
    17,
    18,
    19,
    20,
    21,
    22,
    23,
    24,
    25,
    26,
    27,
    28,
    29,
    30,
    31,
    32,
    33,
    34,
    35,
    36,
    37,
    38,
    39,
    40,
    41,
    42,
    43,
    44,
    45,
    46,
    47,
    48,
    49,
    50,
    51,
    52,
    53,
    54,
    55,
    56,
    57,
    58,
    59,
    60,
    61,
    62,
    63,
    64,
    65,
    66,
    67,
    68,
    69,
    70,
    71,
    72,
    73,
    74,
    75,
    76,
    77,
    78,
    79,
    80,
    81,
    82,
    83,
    84,
    85,
    86,
    87,
    88,
    89,
    90,
    91,
    92,
    93,
    94,
    95,
    96,
    97,
    98,
    99,
    100,
]
"""First 100 digits in the sequence as generated by `range_up`, with sane defaults.
Created with Excel, so this testcase assumes correctness of Excel."""

DOWN = [
    100,
    99,
    98,
    97,
    96,
    95,
    94,
    93,
    92,
    91,
    90,
    89,
    88,
    87,
    86,
    85,
    84,
    83,
    82,
    81,
    80,
    79,
    78,
    77,
    76,
    75,
    74,
    73,
    72,
    71,
    70,
    69,
    68,
    67,
    66,
    65,
    64,
    63,
    62,
    61,
    60,
    59,
    58,
    57,
    56,
    55,
    54,
    53,
    52,
    51,
    50,
    49,
    48,
    47,
    46,
    45,
    44,
    43,
    42,
    41,
    40,
    39,
    38,
    37,
    36,
    35,
    34,
    33,
    32,
    31,
    30,
    29,
    28,
    27,
    26,
    25,
    24,
    23,
    22,
    21,
    20,
    19,
    18,
    17,
    16,
    15,
    14,
    13,
    12,
    11,
    10,
    9,
    8,
    7,
    6,
    5,
    4,
    3,
    2,
    1,
]
"""First 100 digits in the sequence as generated by `range_down`, with sane defaults.
Created with Excel, so this testcase assumes correctness of Excel."""

LONGTERM = [
    1,
    2,
    3,
    4,
    5,
    6,
    8,
    11,
    15,
    20,
    26,
    34,
    45,
    60,
    80,
    106,
    140,
    185,
    245,
    325,
    431,
    571,
    756,
    1001,
    1326,
    1757,
    2328,
    3084,
    4085,
    5411,
    7168,
    9496,
    12580,
    16665,
    22076,
    29244,
    38740,
    51320,
    67985,
    90061,
    119305,
    158045,
    209365,
    277350,
    367411,
    486716,
    644761,
    854126,
    1131476,
    1498887,
    1985603,
    2630364,
    3484490,
    4615966,
    6114853,
    8100456,
    10730820,
    14215310,
    18831276,
    24946129,
    33046585,
    43777405,
    57992715,
    76823991,
    101770120,
    134816705,
    178594110,
    236586825,
    313410816,
    415180936,
    549997641,
    728591751,
    965178576,
    1278589392,
    1693770328,
    2243767969,
    2972359720,
    3937538296,
    5216127688,
    6909898016,
    9153665985,
    12126025705,
    16063564001,
    21279691689,
    28189589705,
    37343255690,
    49469281395,
    65532845396,
    86812537085,
    115002126790,
    152345382480,
    201814663875,
    267347509271,
    354160046356,
    469162173146,
    621507555626,
    823322219501,
    1090669728772,
    1444829775128,
    1913991948274,
]
"""First 100 digits in the long_term_dependency sequence, with sane defaults.
Created with Excel, so this testcase assumes correctness of Excel."""

LONGTERM_SINGLE = [
    1,
    2,
    3,
    4,
    5,
    5,
    10,
    15,
    20,
    25,
    25,
    50,
    75,
    100,
    125,
    125,
    250,
    375,
    500,
    625,
    625,
    1250,
    1875,
    2500,
    3125,
    3125,
    6250,
    9375,
    12500,
    15625,
    15625,
    31250,
    46875,
    62500,
    78125,
    78125,
    156250,
    234375,
    312500,
    390625,
    390625,
    781250,
    1171875,
    1562500,
    1953125,
    1953125,
    3906250,
    5859375,
    7812500,
    9765625,
    9765625,
    19531250,
    29296875,
    39062500,
    48828125,
    48828125,
    97656250,
    146484375,
    195312500,
    244140625,
    244140625,
    488281250,
    732421875,
    976562500,
    1220703125,
    1220703125,
    2441406250,
    3662109375,
    4882812500,
    6103515625,
    6103515625,
    12207031250,
    18310546875,
    24414062500,
    30517578125,
    30517578125,
    61035156250,
    91552734375,
    122070312500,
    152587890625,
    152587890625,
    305175781250,
    457763671875,
    610351562500,
    762939453125,
    762939453125,
    1525878906250,
    2288818359375,
    3051757812500,
    3814697265625,
    3814697265625,
    7629394531250,
    11444091796875,
    15258789062500,
    19073486328125,
    19073486328125,
    38146972656250,
    57220458984375,
    76293945312500,
    95367431640625,
]
"""First 100 digits in the long_term_single_dependency sequence, with sane defaults.
Created with Excel, so this testcase assumes correctness of Excel"""

SHORTTERM_SINGLE = [
    1,
    7,
    49,
    343,
    2401,
    16807,
    117649,
    823543,
    5764801,
    40353607,
    282475249,
    1977326743,
    13841287201,
    96889010407,
    678223072849,
    4747561509943,
    33232930569601,
    232630513987207,
    1628413597910449,
    11398895185373143,
    79792266297612001,
    558545864083284007,
    3909821048582988049,
    27368747340080916343,
    191581231380566414401,
    1341068619663964900807,
    9387480337647754305649,
    65712362363534280139543,
    459986536544739960976801,
    3219905755813179726837607,
    22539340290692258087863249,
    157775382034845806615042743,
    1104427674243920646305299201,
    7730993719707444524137094407,
    54116956037952111668959660849,
    378818692265664781682717625943,
    2651730845859653471779023381601,
    18562115921017574302453163671207,
    129934811447123020117172145698449,
    909543680129861140820205019889143,
    6366805760909027985741435139224001,
    44567640326363195900190045974568007,
    311973482284542371301330321821976049,
    2183814375991796599109312252753832343,
    15286700631942576193765185769276826401,
    107006904423598033356356300384937784807,
    749048330965186233494494102694564493649,
    5243338316756303634461458718861951455543,
    36703368217294125441230211032033660188801,
    256923577521058878088611477224235621321607,
    1798465042647412146620280340569649349251249,
    12589255298531885026341962383987545444758743,
    88124787089723195184393736687912818113311201,
    616873509628062366290756156815389726793178407,
    4318114567396436564035293097707728087552248849,
    30226801971775055948247051683954096612865741943,
    211587613802425391637729361787678676290060193601,
    1481113296616977741464105532513750734030421355207,
    10367793076318844190248738727596255138212949486449,
    72574551534231909331741171093173785967490646405143,
    508021860739623365322188197652216501772434524836001,
    3556153025177363557255317383565515512407041673852007,
    24893071176241544900787221684958608586849291716964049,
    174251498233690814305510551794710260107945042018748343,
    1219760487635835700138573862562971820755615294131238401,
    8538323413450849900970017037940802745289307058918668807,
    59768263894155949306790119265585619217025149412430681649,
    418377847259091645147530834859099334519176045887014771543,
    2928644930813641516032715844013695341634232321209103400801,
    20500514515695490612229010908095867391439626248463723805607,
    143503601609868434285603076356671071740077383739246066639249,
    1004525211269079039999221534496697502180541686174722466474743,
    7031676478883553279994550741476882515263791803223057265323201,
    49221735352184872959961855190338177606846542622561400857262407,
    344552147465294110719732986332367243247925798357929806000836849,
    2411865032257058775038130904326570702735480588505508642005857943,
    16883055225799411425266916330285994919148364119538560494041005601,
    118181386580595879976868414312001964434038548836769923458287039207,
    827269706064171159838078900184013751038269841857389464208009274449,
    5790887942449198118866552301288096257267888893001726249456064921143,
    40536215597144386832065866109016673800875222251012083746192454448001,
    283753509180010707824461062763116716606126555757084586223347181136007,
    1986274564260074954771227439341817016242885890299592103563430267952049,
    13903921949820524683398592075392719113700201232097144724944011875664343,
    97327453648743672783790144527749033795901408624680013074608083129650401,
    681292175541205709486531011694243236571309860372760091522256581907552807,
    4769045228788439966405717081859702655999169022609320640655796073352869649,
    33383316601519079764840019573017918591994183158265244484590572513470087543,
    233683216210633558353880137011125430143959282107856711392134007594290612801,
    1635782513474434908477160959077878011007714974754996979744938053160034289607,
    11450477594321044359340126713545146077054004823284978858214566372120240027249,
    80153343160247310515380886994816022539378033762994852007501964604841680190743,
    561073402121731173607666208963712157775646236340963964052513752233891761335201,
    3927513814852118215253663462745985104429523654386747748367596265637242329346407,
    27492596703964827506775644239221895731006665580707234238573173859460696305424849,
    192448176927753792547429509674553270117046659064950639670012217016224874137973943,
    1347137238494276547832006567721872890819326613454654477690085519113574118965817601,
    9429960669459935834824045974053110235735286294182581343830598633795018832760723207,
    66009724686219550843768321818371771650147004059278069406814190436565131829325062449,
    462068072803536855906378252728602401551029028414946485847699333055955922805275437143,
]
"""First 100 digits in the short_term_single_dependency sequence, with constant being 7.
Cannot be recreated with Excel due to precision issues - coded up instead."""