Last modified Tuesday, January 11, 2000 5:04 pm

Pell's sequence.

1,2,5,12,29,70,169,408,985,2378,5741,13860,33461,80782,195025,470832,1136689,2744210,
6625109,15994428,38613965,93222358,225058681,543339720,1311738121,3166815962,7645370045,
18457556052,44560482149,107578520350,259717522849,627013566048,1513744654945,
3654502875938,8822750406821,21300003689580,51422757785981,124145519261542,
299713796309065,723573111879672,1746860020068409,4217293152016490,10181446324101389,
24580185800219268,59341817924539925,143263821649299118,345869461223138161,
835002744095575440,2015874949414289041,4866752642924153522,11749380235262596085,
28365513113449345692,68480406462161287469,165326326037771920630,399133058537705128729,
963592443113182178088,2326317944764069484905,5616228332641321147898,
13558774610046711780701,32733777552734744709300,79026329715516201199301,
190786436983767147107902,460599203683050495415105,1111984844349868137938112,
2684568892382786771291329,6481122629115441680520770,15646814150613670132332869,
37774750930342781945186508,91196316011299234022705885,220167382952941249990598278,
531531081917181734003902441,1283229546787304717998403160,3097990175491791170000708761,
7479209897770887057999820682,18056409971033565286000350125,43592029839838017630000520932,
105240469650709600546001391989,254072969141257218722003304910,
613386407933224037990008001809,1480845785007705294702019308528,
3575077977948634627394046618865,8631001740904974549490112546258,
20837081459758583726374271711381,50305164660422142002238655969020,
121447410780602867730851583649421,293199986221627877463941823267862,
707847383223858622658735230185145,1708894752669345122781412283638152,
4125636888562548868221559797461449,9960168529794442859224531878561050,
24045973948151434586670623554583549,58052116426097312032565778987728148,
140150206800346058651802181530039845,338352530026789429336170142047807838,
816855266853924917324142465625655521,1972063063734639263984455073299118880,
4760981394323203445293052612223893281,11494025852381046154570560297746905442,
27749033099085295754434173207717704165,66992092050551637663438906713182313772,...

s=4:
period = 4; pre-periodic length = 0 [1,2,1,4] ...



shaft utilization:

    1:  50%  ++++++++++++++++++++++++++++++++++++++++++++++++++
    2:  25%  +++++++++++++++++++++++++
    3:   0%  
    4:  25%  +++++++++++++++++++++++++

s=5:
period = 12; pre-periodic length = 0 [1,2,5,2,4,5,4,3,5,3,1,5] ...



shaft utilization:

    1:  17%  +++++++++++++++++
    2:  18%  ++++++++++++++++++
    3:  16%  ++++++++++++++++
    4:  16%  ++++++++++++++++
    5:  33%  +++++++++++++++++++++++++++++++++

s=6:
period = 8; pre-periodic length = 0 [1,2,5,6,5,4,1,6] ...



shaft utilization:

    1:  25%  +++++++++++++++++++++++++
    2:  13%  +++++++++++++
    3:   0%  
    4:  12%  ++++++++++++
    5:  25%  +++++++++++++++++++++++++
    6:  25%  +++++++++++++++++++++++++

s=7:
period = 6; pre-periodic length = 0 [1,2,5,5,1,7] ...



shaft utilization:

    1:  33%  +++++++++++++++++++++++++++++++++
    2:  17%  +++++++++++++++++
    3:   0%  
    4:   0%  
    5:  34%  ++++++++++++++++++++++++++++++++++
    6:   0%  
    7:  16%  ++++++++++++++++

s=8:
period = 8; pre-periodic length = 0 [1,2,5,4,5,6,1,8] ...



shaft utilization:

    1:  25%  +++++++++++++++++++++++++
    2:  13%  +++++++++++++
    3:   0%  
    4:  13%  +++++++++++++
    5:  25%  +++++++++++++++++++++++++
    6:  12%  ++++++++++++
    7:   0%  
    8:  12%  ++++++++++++

s=9:
period = 24; pre-periodic length = 0 [1,2,5,3,2,7,7,3,4,2,8,9,8,7,4,6,7,2,2,6,5,7,1,9] ...



shaft utilization:

    1:   9%  +++++++++
    2:  21%  +++++++++++++++++++++
    3:   9%  +++++++++
    4:   8%  ++++++++
    5:   9%  +++++++++
    6:   8%  ++++++++
    7:  20%  ++++++++++++++++++++
    8:   8%  ++++++++
    9:   8%  ++++++++

s=10:
period = 12; pre-periodic length = 0 [1,2,5,2,9,10,9,8,5,8,1,10] ...



shaft utilization:

    1:  17%  +++++++++++++++++
    2:  18%  ++++++++++++++++++
    3:   0%  
    4:   0%  
    5:  17%  +++++++++++++++++
    6:   0%  
    7:   0%  
    8:  16%  ++++++++++++++++
    9:  16%  ++++++++++++++++
   10:  16%  ++++++++++++++++

s=11:
period = 24; pre-periodic length = 0 [1,2,5,1,7,4,4,1,6,2,10,11,10,9,6,10,4,7,7,10,5,9,1,11] ...



shaft utilization:

    1:  18%  ++++++++++++++++++
    2:   9%  +++++++++
    3:   0%  
    4:  12%  ++++++++++++
    5:   9%  +++++++++
    6:   8%  ++++++++
    7:  12%  ++++++++++++
    8:   0%  
    9:   8%  ++++++++
   10:  16%  ++++++++++++++++
   11:   8%  ++++++++

s=12:
period = 8; pre-periodic length = 0 [1,2,5,12,5,10,1,12] ...



shaft utilization:

    1:  25%  +++++++++++++++++++++++++
    2:  13%  +++++++++++++
    3:   0%  
    4:   0%  
    5:  25%  +++++++++++++++++++++++++
    6:   0%  
    7:   0%  
    8:   0%  
    9:   0%  
   10:  12%  ++++++++++++
   11:   0%  
   12:  25%  +++++++++++++++++++++++++

s=13:
period = 28; pre-periodic length = 0 [1,2,5,12,3,5,13,5,10,12,8,2,12,13,12,11,8,1,10,8,13,8,3,1,5,11,1,13] ...



shaft utilization:

    1:  13%  +++++++++++++
    2:   8%  ++++++++
    3:   7%  +++++++
    4:   0%  
    5:  15%  +++++++++++++++
    6:   0%  
    7:   0%  
    8:  13%  +++++++++++++
    9:   0%  
   10:   7%  +++++++
   11:   7%  +++++++
   12:  16%  ++++++++++++++++
   13:  14%  ++++++++++++++

s=14:
period = 6; pre-periodic length = 0 [1,2,5,12,1,14] ...



shaft utilization:

    1:  33%  +++++++++++++++++++++++++++++++++
    2:  17%  +++++++++++++++++
    3:   0%  
    4:   0%  
    5:  17%  +++++++++++++++++
    6:   0%  
    7:   0%  
    8:   0%  
    9:   0%  
   10:   0%  
   11:   0%  
   12:  17%  +++++++++++++++++
   13:   0%  
   14:  16%  ++++++++++++++++

s=15:
period = 24; pre-periodic length = 0 [1,2,5,12,14,10,4,3,10,8,11,15,11,7,10,12,4,5,14,3,5,13,1,15] ...



shaft utilization:

    1:   9%  +++++++++
    2:   5%  +++++
    3:   8%  ++++++++
    4:   8%  ++++++++
    5:  13%  +++++++++++++
    6:   0%  
    7:   4%  ++++
    8:   4%  ++++
    9:   0%  
   10:  12%  ++++++++++++
   11:   8%  ++++++++
   12:   9%  +++++++++
   13:   4%  ++++
   14:   8%  ++++++++
   15:   8%  ++++++++

s=16:
period = 16; pre-periodic length = 0 [1,2,5,12,13,6,9,8,9,10,13,4,5,14,1,16] ...



shaft utilization:

    1:  13%  +++++++++++++
    2:   7%  +++++++
    3:   0%  
    4:   6%  ++++++
    5:  13%  +++++++++++++
    6:   6%  ++++++
    7:   0%  
    8:   6%  ++++++
    9:  12%  ++++++++++++
   10:   6%  ++++++
   11:   0%  
   12:   7%  +++++++
   13:  12%  ++++++++++++
   14:   6%  ++++++
   15:   0%  
   16:   6%  ++++++

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e-mail: ralph@cs.arizona.edu

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