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

1,2

Comments

Sequence extended to n = 1 using formula.

Links

Table of n, a(n) for n=1..25.

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).

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)

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]

Crossrefs

Cf. A286182, A000129, A002203.

Sequence in context: A181345 A193125 A305868 * A319324 A059435 A192621

Adjacent sequences: A356827 A356828 A356829 * A356831 A356832 A356833

Keyword

nonn

Author

Eric W. Weisstein, Aug 30 2022

Extensions

More terms from Pontus von Brömssen, Aug 30 2022

Status

approved