A356829 Number of vertex cuts in the n-Möbius ladder.

0, 0, 8, 82, 512, 2644, 12364, 54598, 232772, 970520, 3988624, 16239066, 65709256, 264814140, 1064414100, 4271035662, 17118683020, 68563527616, 274481537112, 1098506723042, 4395504614544, 17585769696164, 70352578566620, 281434319454038, 1125797816327892

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, Moebius Ladder
• 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. A286185.

Programs

Mathematica

Table[4^n + n - LucasL[n, 2] - 3 n Fibonacci[n, 2], {n, 20}]
LinearRecurrence[{10, -35, 48, -11, -22, 7, 4}, {0, 0, 8, 82, 512, 2644, 12364}, 20]
CoefficientList[Series[2 x^2 (-4 - x + 14 x^2 - 5 x^3 + 2 x^4)/((-1 + x)^2 (-1 + 4 x) (-1 + 2 x + x^2)^2), {x, 0, 20}], x]

Formula

a(n) = 2^(2*n) - A286185(n) - 1. - Pontus von Brömssen, Aug 30 2022

a(n) = 4^n + n - LucasL(n, 2) - 3*n*Fibonacci(n, 2).

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^3*(-4-x+14*x^2-5*x^3+2*x^4)/((-1+x)^2*(-1+4*x)*(-1+2*x+x^2)^2).

Extensions

More terms from Pontus von Brömssen, Aug 30 2022