A234617 Numbers of undirected cycles in the 2n-crossed prism graph.

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

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: A266976 A352739 A117999 * A028379 A332751 A263942

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