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 A234617 Numbers of undirected cycles in the 2n-crossed prism graph. 2
 6, 28, 107, 380, 1345, 4878, 18219, 69736, 271589, 1069538, 4240351, 16877532, 67325913, 268902358, 1074741203, 4297097168, 17184391117, 68729044938, 274898091975, 1099554095044, 4398135640001, 17592372690878, 70369134247867, 281475790405560, 1125901601341365 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequence extended via recurrence to start at n = 1. - Andrew Howroyd, May 09 2017 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 Eric Weisstein's World of Mathematics, Crossed Prism Graph Eric Weisstein's World of Mathematics, Graph Cycle Index entries for linear recurrences with constant coefficients, signature (10, -37, 64, -52, 16). FORMULA From Andrew Howroyd, May 09 2017 (Start) a(n) = 10*a(n-1)-37*a(n-2)+64*a(n-3)-52*a(n-4)+16*a(n-5) for n>5. G.f.: x*(24*x^4-38*x^3+49*x^2-32*x+6)/((1-4*x)*(x-1)^2*(2*x-1)^2). (End) a(n) = 2^(n-1)+4^n+(2^(n+1)-3)*n. - Eric W. Weisstein, May 11 2017 MATHEMATICA Rest@ CoefficientList[Series[x (24 x^4 - 38 x^3 + 49 x^2 - 32 x + 6)/((1 - 4 x) (x - 1)^2*(2 x - 1)^2), {x, 0, 25}], x] (* or *) LinearRecurrence[{10, -37, 64, -52, 16}, {6, 28, 107, 380, 1345}, 25] (* Michael De Vlieger, May 09 2017 *) Table[2^(n - 1) + 4^n + (2^(n + 1) - 3) n, {n, 20}] (* Eric W. Weisstein, May 11 2017 *) PROG (PARI) Vec((24*x^4-38*x^3+49*x^2-32*x+6)/((1-4*x)*(x-1)^2*(2*x-1)^2)+O(x^50)) \\ Andrew Howroyd, May 09 2017 CROSSREFS Cf. A137885. Sequence in context: A134416 A266976 A117999 * A028379 A263942 A326138 Adjacent sequences:  A234614 A234615 A234616 * A234618 A234619 A234620 KEYWORD nonn AUTHOR Eric W. Weisstein, Dec 28 2013 EXTENSIONS Offset corrected and a(1), a(10)-a(25) from Andrew Howroyd, May 09 2017 STATUS approved

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Last modified October 18 04:57 EDT 2019. Contains 328145 sequences. (Running on oeis4.)