A356828 Number of vertex cuts in the n-ladder graph P_2 x P_n.

0, 2, 23, 147, 748, 3414, 14719, 61495, 252364, 1024938, 4137207, 16639339, 66775964, 267631726, 1071801407, 4290282671, 17168559452, 68692172578, 274811988823, 1099352487299, 4397662311948, 17591258505542, 70366504900671, 281469570617703, 1125886855379628

Offset: 1

Author

Eric W. Weisstein, Aug 30 2022

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Ladder Graph
• Eric Weisstein's World of Mathematics, Vertex Cut
• Index entries for linear recurrences with constant coefficients, signature (8,-20,16,1,-4).

Crossrefs

Cf. A059020.

Programs

Mathematica

Table[4^n + 2 n + (10 - LucasL[n + 3, 2])/4, {n, 20}]
LinearRecurrence[{8, -20, 16, 1, -4}, {0, 2, 23, 147, 748}, 20]
CoefficientList[Series[x (2 + x) (1 + 3 x)/((-1 + x)^2 (-1 + 4 x) (-1 + 2 x + x^2)), {x, 0, 20}], x]

Formula

a(n) = 4^n + 2*n + (10 - LucasL(n + 3, 2))/4.

a(n) = 8*a(n-1) - 20*a(n-2) + 16*a(n-3) + a(n-4) - 4*a(n-5).

G.f.: x^2*(2+x)*(1+3*x)/((-1+x)^2*(-1+4*x)*(-1+2*x + x^2)).

a(n) = 2^(2*n) - A059020(n) - 1. - Pontus von Brömssen, Aug 30 2022