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 A005390 Number of Hamiltonian circuits on 2n X 6 rectangle. (Formerly M5264) 2
 1, 37, 1072, 32675, 1024028, 32463802, 1033917350, 32989068162, 1053349394128, 33643541208290, 1074685815276400, 34330607094625734, 1096704136430950646, 35034883701169366742, 1119214052513009716324, 35754123580486507079548 (list; graph; refs; listen; history; text; internal format)
 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:=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. = 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 EXTENSIONS More terms from André Pönitz (poenitz(AT)htwm.de), Jun 11 2003 STATUS approved

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Last modified February 3 05:52 EST 2023. Contains 360024 sequences. (Running on oeis4.)