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A356828
Number of vertex cuts in the n-ladder graph P_2 x P_n.
1
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
1,2
LINKS
Eric Weisstein's World of Mathematics, Ladder Graph
Eric Weisstein's World of Mathematics, Vertex Cut
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
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]
CROSSREFS
Cf. A059020.
Sequence in context: A193981 A235594 A053299 * A220239 A189977 A130547
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 30 2022
STATUS
approved