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

Author

Eric W. Weisstein, Aug 19 2022

Keywords

• nonn

Comments

Sequence extended to n = 1 using formula.

Links

• 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).

Crossrefs

Cf. A286183.

Programs

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]

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

Extensions

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