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 A003772 Number of Hamiltonian paths in K_4 X P_n. 1
 12, 408, 6648, 90672, 1103088, 12509256, 135409896, 1419480288, 14545113696, 146607233784, 1460033574744, 14411647534224, 141321405768144, 1379055205227432, 13408489143753672, 130019327919243840, 1258252792162873152, 12158637295940721240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 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. F. Faase, Results from the counting program Index entries for linear recurrences with constant coefficients, signature (23,-173,421,62,-132,24). FORMULA Faase gives a 6-term linear recurrence on his web page: a(1) = 12, a(2) = 408, a(3) = 6648, a(4) = 90672, a(5) = 1103088, a(6) = 12509256, a(7) = 135409896 and a(n) = 23a(n-1) - 173a(n-2) + 421a(n-3) + 62a(n-4) - 132a(n-5) + 24a(n-6). G.f.: 12*x*(24*x^6-164*x^5+398*x^4-275*x^3+55*x^2-11*x-1)/((2*x^2-7*x+1)^2*(6*x^2+9*x-1)). [Colin Barker, Aug 30 2012] MATHEMATICA CoefficientList[Series[12(24 x^6 - 164 x^5 + 398 x^4 - 275 x^3 + 55 x^2 - 11 x - 1)/((2 x^2 - 7 x + 1)^2 (6 x^2 + 9 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 14 2013 *) LinearRecurrence[{23, -173, 421, 62, -132, 24}, {12, 408, 6648, 90672, 1103088, 12509256, 135409896}, 20] (* Harvey P. Dale, Jun 11 2019 *) CROSSREFS Sequence in context: A202788 A285028 A292784 * A211078 A299382 A197038 Adjacent sequences:  A003769 A003770 A003771 * A003773 A003774 A003775 KEYWORD nonn,easy AUTHOR EXTENSIONS Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009 STATUS approved

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Last modified October 14 07:00 EDT 2019. Contains 327995 sequences. (Running on oeis4.)