A356830 Number of vertex cuts in the n-prism graph.

0, 2, 12, 88, 520, 2654, 12376, 54612, 232788, 970538, 3988644, 16239088, 65709280, 264814166, 1064414128, 4271035692, 17118683052, 68563527650, 274481537148, 1098506723080, 4395504614584, 17585769696206, 70352578566664, 281434319454084, 1125797816327940

Offset: 1

Author

Eric W. Weisstein, Aug 30 2022

Keywords

• nonn

Comments

Sequence extended to n = 1 using formula.

Links

• Eric Weisstein's World of Mathematics, Prism Graph
• Eric Weisstein's World of Mathematics, Vertex Cut
• Index entries for linear recurrences with constant coefficients, signature (10,-35,48,-11,-22,7,4).

Crossrefs

Cf. A286182, A000129, A002203.

Programs

Mathematica

Table[4^n + 3 n - 3 n Fibonacci[n, 2] - LucasL[n, 2] - 2, {n, 20}]
LinearRecurrence[{10, -35, 48, -11, -22, 7, 4}, {0, 2, 12, 88, 520, 2654, 12376}, 20]
CoefficientList[Series[2 x (-1 + 4 x - 19 x^2 + 18 x^3 + 10 x^4 + 6 x^5)/((-1 + x)^2 (-1 + 4 x) (-1 + 2 x + x^2)^2), {x, 0, 20}], x]

Formula

a(n) = 2^(2*n) - A286182(n) - 1. - Pontus von Brömssen, Aug 30 2022

From Eric W. Weisstein, Aug 31 2022: (Start)

a(n) = 4^n + 3*n - 3*n*Fibonacci(n, 2) - Lucas(n, 2), where Fibonacci(n, 2) = A000129(n) and Lucas(n, 2) = A002203(n).

a(n) = 10*a(n-1) - 35*a(n-2) + 48*a(n-3) - 11*a(n-4) - 22*a(n-5) + 7*a(n-6) + 4*a(n-7).

G.f.: 2*x^2*(-1 + 4*x - 19*x^2 + 18*x^3 + 10*x^4 + 6*x^5)/((-1 + x)^2*(-1 + 4*x)*(-1 + 2*x + x^2)^2). (End)

Extensions

More terms from Pontus von Brömssen, Aug 30 2022