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A003778 Number of Hamiltonian paths in P_5 X P_n. 6
1, 22, 132, 1006, 4324, 26996, 109722, 602804, 2434670, 12287118, 49852352, 237425498, 969300694, 4434629912, 18203944458, 80978858522, 333840165288, 1456084764388, 6021921661718, 25904211802080 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
LINKS
F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
A. Kloczkowski, and R. L. Jernigan, Transfer matrix method for enumeration and generation of compact self-avoiding walks. I. Square lattices, The Journal of Chemical Physics 109, 5134 (1998); doi: 10.1063/1.477128.
FORMULA
Faase gives a 36-term linear recurrence on his web page:
a(1) = 1,
a(2) = 22,
a(3) = 132,
a(4) = 1006,
a(5) = 4324,
a(6) = 26996,
a(7) = 109722,
a(8) = 602804,
a(9) = 2434670,
a(10) = 12287118,
a(11) = 49852352,
a(12) = 237425498,
a(13) = 969300694,
a(14) = 4434629912,
a(15) = 18203944458,
a(16) = 80978858522,
a(17) = 333840165288,
a(18) = 1456084764388,
a(19) = 6021921661718,
a(20) = 25904211802080,
a(21) = 107378816068904,
a(22) = 457440612631750,
a(23) = 1899305396852550,
a(24) = 8036345146341508,
a(25) = 33405640842497978,
a(26) = 140677778437397166,
a(27) = 585243342550350368,
a(28) = 2456482541007655088,
a(29) = 10225087180260916062,
a(30) = 42821044456634131964,
a(31) = 178310739623644629736,
a(32) = 745570951093506967610,
a(33) = 3105442902100584328222,
a(34) = 12970906450154764259728,
a(35) = 54035954199253554652658,
a(36) = 225534416271325317632922,
a(37) = 939676160294548239862008,
a(38) = 3920063808158344161168316 and
a(n) = 9a(n-1) + 13a(n-2) - 328a(n-3) + 412a(n-4) + 4606a(n-5)
- 11333a(n-6) - 30993a(n-7) + 116054a(n-8) + 91896a(n-9) - 647749a(n-10)
+ 46716a(n-11) + 2183660a(n-12) - 1288032a(n-13) - 4582138a(n-14) + 4554646a(n-15)
+ 5907135a(n-16) - 8495755a(n-17) - 4382389a(n-18) + 9710124a(n-19) + 1499560a(n-20)
- 7358998a(n-21) + 149939a(n-22) + 4121575a(n-23) - 474900a(n-24) - 1872534a(n-25)
+ 392241a(n-26) + 637672a(n-27) - 187640a(n-28) - 147856a(n-29) + 48980a(n-30)
+ 28332a(n-31) - 13032a(n-32) - 216a(n-33) + 756a(n-34) - 864a(n-35)
+ 432a(n-36).
CROSSREFS
Row n=5 of A332307.
Sequence in context: A095694 A233060 A299520 * A254698 A041936 A254699
KEYWORD
nonn
AUTHOR
EXTENSIONS
Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009
STATUS
approved

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Last modified April 23 02:53 EDT 2024. Contains 371906 sequences. (Running on oeis4.)