A005390 Number of Hamiltonian circuits on 2n X 6 rectangle.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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).

Crossrefs

Cf. A145401.

Programs

Magma

R:=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

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 *)

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. = PowerSeriesRing(ZZ, prec)
    return P( g(x) ).list()
a=A005390_list(40); a[1:] # G. C. Greubel, Nov 17 2022

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

Extensions

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