A005390 Number of Hamiltonian circuits on 2n X 6 rectangle. (Formerly M5264)

1, 37, 1072, 32675, 1024028, 32463802, 1033917350, 32989068162, 1053349394128, 33643541208290, 1074685815276400, 34330607094625734, 1096704136430950646, 35034883701169366742, 1119214052513009716324, 35754123580486507079548

Offset

1,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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).

Formula

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

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A145401.

Sequence in context: A218764 A217454 A101631 * A253245 A168166 A168165

Adjacent sequences: A005387 A005388 A005389 * A005391 A005392 A005393

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from André Pönitz (poenitz(AT)htwm.de), Jun 11 2003

Status

approved