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 A308137 Number of (undirected) Hamiltonian paths on the n-prism graph. 1
 30, 72, 130, 228, 350, 528, 738, 1020, 1342, 1752, 2210, 2772, 3390, 4128, 4930, 5868, 6878, 8040, 9282, 10692, 12190, 13872, 15650, 17628, 19710, 22008, 24418, 27060, 29822, 32832, 35970, 39372, 42910, 46728, 50690, 54948, 59358, 64080, 68962, 74172, 79550 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 LINKS Colin Barker, Table of n, a(n) for n = 3..1000 Eric Weisstein's World of Mathematics, Hamiltonian Path Eric Weisstein's World of Mathematics, Prism Graph Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1). FORMULA a(n) = A124350(n)/2. From Colin Barker, Jul 19 2019: (Start) G.f.: 2*x^3*(15 + 6*x - 22*x^2 + 8*x^3 + 11*x^4 - 6*x^5) / ((1 - x)^4*(1 + x)^2). a(n) = n*(3 + (-1)^n + 2*n^2) / 2. a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>8. (End) PROG (PARI) Vec(2*x^3*(15 + 6*x - 22*x^2 + 8*x^3 + 11*x^4 - 6*x^5) / ((1 - x)^4*(1 + x)^2) + O(x^30)) \\ Colin Barker, Jul 19 2019 CROSSREFS Cf. A124350. Sequence in context: A071142 A218327 A259753 * A179321 A039517 A185479 Adjacent sequences:  A308134 A308135 A308136 * A308138 A308139 A308140 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, May 14 2019 EXTENSIONS More terms from Colin Barker, Jul 19 2019 STATUS approved

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Last modified January 22 13:36 EST 2020. Contains 331149 sequences. (Running on oeis4.)