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
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).
Programs
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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 *) -
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
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
Extensions
a(0)-a(2) prepended and a(10) onwards from Andrew Howroyd, Nov 26 2024
Comments