A378296 Number of cyclic edge cuts in the n-ladder graph.

0, 0, 0, 1, 32, 612, 9160, 118608, 1395872, 15356032, 160695936, 1618315776, 15811200000, 150746793984, 1408654503936, 12944302796800, 117272743264256, 1049672527036416, 9297570440642560, 81607973259116544, 710607254147956736, 6144222507232657408, 52794307266655813632

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Eric Weisstein's World of Mathematics, Cyclic Edge Cut.

Eric Weisstein's World of Mathematics, Ladder Graph.

Index entries for linear recurrences with constant coefficients, signature (30,-348,1936,-5168,5856,-2880,512).

Formula

G.f.: x^4*(1 + 2*x)/((1 - 8*x)*(1 - 8*x + 4*x^2)^2*(1 - 6*x + 4*x^2)). - Andrew Howroyd, May 28 2025

a(n) = 30*a(n-1)-348*a(n-2)+1936*a(n-3)-5168*a(n-4)+5856*a(n-5)-2880*a(n-6)+512*a(n-7). - Eric W. Weisstein, Aug 28 2025

Mathematica

Table[1/960 (5 (4 - 2 Sqrt[3])^n (-24 + 11 Sqrt[3]) - 5 (2 (2 + Sqrt[3]))^n (24 + 11 Sqrt[3]) + 15 2^(2 + n) (4^(1 + n) - Fibonacci[2 n]) - 15 2^(1 + n) n Fibonacci[1 + 2 n, Sqrt[2]]), {n, 20}] // FullSimplify (* Eric W. Weisstein, Aug 28 2025 *)
LinearRecurrence[{30, -348, 1936, -5168, 5856, -2880, 512}, {0, 0, 0, 1, 32, 612, 9160}, 20] (* Eric W. Weisstein, Aug 28 2025 *)
CoefficientList[Series[(-1 - 2 x) x^3/((1 - 8 x + 4 x^2)^2 (-1 + 14 x - 52 x^2 + 32 x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 28 2025 *)

Prog

(PARI) concat([0, 0, 0], Vec((1 + 2*x)/((1 - 8*x)*(1 - 8*x + 4*x^2)^2*(1 - 6*x + 4*x^2)) + O(x^20))) \\ Andrew Howroyd, May 28 2025

Crossrefs

Sequence in context: A036903 A208828 A013699 * A283279 A004337 A292880

Adjacent sequences: A378293 A378294 A378295 * A378297 A378298 A378299

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 22 2024

Extensions

a(10) from Eric W. Weisstein, Dec 04 2024

a(11) onwards from Andrew Howroyd, May 28 2025

Status

approved