A377638 Number of edge cuts in the n-gear graph.

1, 5, 45, 419, 3665, 30795, 253137, 2056059, 16589761, 133362635, 1069841265, 8572141979, 68638314785, 549385589355, 4396357712337, 35176668544059, 281439836584321, 2251639520143115, 18013667322023985, 144111852725650139, 1152906290230734305, 9223302635674623915

Offset

0,2

Comments

The sequence has been extended to n=0 using the recurrence. - Andrew Howroyd, Nov 26 2024

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Edge Cut.

Eric Weisstein's World of Mathematics, Gear Graph.

Index entries for linear recurrences with constant coefficients, signature (14,-55,58,-16).

Formula

G.f.: (1 - 9*x + 30*x^2 + 6*x^3)/((1 - x)*(1 - 8*x)*(1 - 5*x + 2*x^2)). - Andrew Howroyd, Nov 26 2024

a(n) = 14*a(n-1)-55*a(n-2)+58*a(n-3)-16*a(n-4). (* Eric W. Weisstein, Dec 01 2024 *)

Mathematica

Table[2 + 8^n - (1/2 (5 - Sqrt[17]))^n - (1/2 (5 + Sqrt[17]))^n, {n, 0, 20}] // Expand (* Eric W. Weisstein, Dec 01 2024 *)
LinearRecurrence[{14, -55, 58, -16}, {1, 5, 45, 419}, 20] (* Eric W. Weisstein, Dec 01 2024 *)
CoefficientList[Series[(1 - 9 x + 30 x^2 + 6 x^3)/((-1 + x) (-1 + 8 x) (1 - 5 x + 2 x^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2024 *)

Prog

(PARI) Vec((1 - 9*x + 30*x^2 + 6*x^3)/((1 - x)*(1 - 8*x)*(1 - 5*x + 2*x^2)) + O(x^22)) \\ Andrew Howroyd, Nov 26 2024

Crossrefs

Cf. A356200, A362516.

Sequence in context: A173558 A022022 A058410 * A005979 A165225 A121272

Adjacent sequences: A377635 A377636 A377637 * A377639 A377640 A377641

Keyword

nonn,easy,changed

Author

Eric W. Weisstein, Nov 03 2024

Extensions

a(0)-a(2) prepended and a(10) onwards from Andrew Howroyd, Nov 26 2024

Status

approved