A356644 Number of vertex cuts in the n-antiprism graph.

0, 0, 3, 48, 360, 2057, 10276, 47552, 209871, 898168, 3765080, 15560725, 63681228, 258826128, 1046920155, 4220390592, 16973219016, 68148598817, 273305152756, 1095189435488, 4386195036135, 17559755662600, 70280167711928, 281233465458733, 1125242449638300, 4501812479503152

Offset

1,3

Comments

Sequence extended to n = 1 using formula.

Links

Table of n, a(n) for n=1..26.

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Vertex Cut

Index entries for linear recurrences with constant coefficients, signature (12,-56,130,-160,104,-33,4).

Formula

a(n) = 2^(2*n) - A286183(n)-1. - Pontus von Brömssen, Aug 21 2022

a(n) = 4^n + 2*n - LucasL(2*n) - 2*n*Fibonacci(2 n) - 1. - Eric W. Weisstein, Aug 30 2022

a(n) = 12*a(n-1) - 56*a(n-2) + 130*a(n-3) -160*a(n-4) + 104*a(n-5) - 33*a(n-6) + 4*a(n-7). - Eric W. Weisstein, Aug 30 2022

G.f.: x^3*(-3-12*x+48*x^2-35*x^3+8*x^4)/((-1+4*x)*(-1+4*x-4*x^2+x^3)^2). - Eric W. Weisstein, Aug 30 2022

Mathematica

Table[4^n + 2 n - LucasL[2 n] - 2 n Fibonacci[2 n] - 1, {n, 20}]
LinearRecurrence[{12, -56, 130, -160, 104, -33, 4}, {0, 0, 3, 48, 360, 2057, 10276}, 20]
CoefficientList[Series[x^2 (-3 - 12 x + 48 x^2 - 35 x^3 + 8 x^4)/((-1 + x)^2 (-1 + 4 x) (1 - 3 x + x^2)^2), {x, 0, 20}], x]

Crossrefs

Cf. A286183.

Sequence in context: A219056 A230962 A073982 * A354132 A335178 A260347

Adjacent sequences: A356641 A356642 A356643 * A356645 A356646 A356647

Keyword

nonn

Author

Eric W. Weisstein, Aug 19 2022

Extensions

a(13)-a(26) (based on A286183) from Pontus von Brömssen, Aug 21 2022

Status

approved