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A005390
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Number of Hamiltonian circuits on 2n X 6 rectangle.
(Formerly M5264)
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2
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1, 37, 1072, 32675, 1024028, 32463802, 1033917350, 32989068162, 1053349394128, 33643541208290, 1074685815276400, 34330607094625734, 1096704136430950646, 35034883701169366742, 1119214052513009716324, 35754123580486507079548
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..660
Andre Poenitz, Some software
T. G. Schmalz, G. E. Hite and D. J. Klein, Compact self-avoiding circuits on two-dimensional lattices, J. Phys. A 17 (1984), 445-453.
Index entries for linear recurrences with constant coefficients, signature (53,-802,4463,-10928,13708,-12157,7032,-11272, 15064,-13336,5948,-792,-96,-4).
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FORMULA
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a(n) = A145401(2*n). - Sean A. Irvine, Jun 11 2016
G.f.: x*(1 - 16*x - 87*x^2 + 1070*x^3 - 2206*x^4 + 1960*x^5 - 2448*x^6 + 1053*x^7 + 392*x^8 - 1517*x^9 + 1012*x^10 - 120*x^11 - 28*x^12 - 2*x^13)/(1 - 53*x + 802*x^2 - 4463*x^3 + 10928*x^4 - 13708*x^5 + 12157*x^6 - 7032*x^7 + 11272*x^8 - 15064*x^9 + 13336*x^10 - 5948*x^11 + 792*x^12 + 96*x^13 + 4*x^14). - G. C. Greubel, Nov 18 2022
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MATHEMATICA
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Rest@CoefficientList[Series[x*(1 -16*x -87*x^2 +1070*x^3 -2206*x^4 +1960*x^5 -2448*x^6 +1053*x^7 +392*x^8 -1517*x^9 +1012*x^10 -120*x^11 -28*x^12 -2*x^13)/(1 -53*x + 802*x^2 -4463*x^3 +10928*x^4 -13708*x^5 +12157*x^6 -7032*x^7 +11272*x^8 -15064*x^9 +13336*x^10 -5948*x^11 +792*x^12 +96*x^13 +4*x^14), {x, 0, 40}], x] (* G. C. Greubel, Nov 17 2022 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1 -16*x -87*x^2 +1070*x^3 -2206*x^4 +1960*x^5 -2448*x^6 +1053*x^7 +392*x^8 -1517*x^9 +1012*x^10 -120*x^11 -28*x^12 -2*x^13)/(1 -53*x + 802*x^2 -4463*x^3 +10928*x^4 -13708*x^5 +12157*x^6 -7032*x^7 +11272*x^8 -15064*x^9 +13336*x^10 -5948*x^11 +792*x^12 +96*x^13 +4*x^14) )); // G. C. Greubel, Nov 17 2022
(SageMath)
def g(x): return x*(1 -16*x -87*x^2 +1070*x^3 -2206*x^4 +1960*x^5 -2448*x^6 +1053*x^7 +392*x^8 -1517*x^9 +1012*x^10 -120*x^11 -28*x^12 -2*x^13)/(1 -53*x + 802*x^2 -4463*x^3 +10928*x^4 -13708*x^5 +12157*x^6 -7032*x^7 +11272*x^8 -15064*x^9 +13336*x^10 -5948*x^11 +792*x^12 +96*x^13 +4*x^14)
def A005390_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( g(x) ).list()
a=A005390_list(40); a[1:] # G. C. Greubel, Nov 17 2022
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CROSSREFS
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Cf. A145401.
Sequence in context: A218764 A217454 A101631 * A253245 A168166 A168165
Adjacent sequences: A005387 A005388 A005389 * A005391 A005392 A005393
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from André Pönitz (poenitz(AT)htwm.de), Jun 11 2003
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STATUS
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approved
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