A290593 Number of maximal independent vertex sets (and minimal vertex covers) in the n-antiprism graph.

3, 12, 15, 31, 49, 92, 156, 279, 484, 855, 1495, 2629, 4608, 8092, 14195, 24916, 43719, 76727, 134641, 236284, 414644, 727655, 1276940, 2240879, 3932463, 6900997, 12110400, 21252276, 37295139, 65448412, 114853951, 201554639, 353703729, 620706780, 1089264460, 1911525879

Offset

3,1

Links

Table of n, a(n) for n=3..38.

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set

Eric Weisstein's World of Mathematics, Minimal Vertex Cover

Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 1).

Formula

a(n) = a(n-1) + a(n-2) + a(n-4).

G.f.: (x^3 (-3 - 9 x - 4 x^3))/(-1 + x + x^2 + x^4).

Mathematica

Table[2 (-1)^n + RootSum[-1 + # - 2 #^2 + #^3 &, #^n &], {n, 3, 20}]
LinearRecurrence[{1, 1, 0, 1}, {3, 12, 15, 31}, 20]
CoefficientList[Series[(-3 - 9 x - 4 x^3)/(-1 + x + x^2 + x^4), {x, 0, 20}], x]

Crossrefs

Sequence in context: A329575 A022380 A331074 * A005392 A001196 A330941

Adjacent sequences: A290590 A290591 A290592 * A290594 A290595 A290596

Keyword

nonn

Author

Eric W. Weisstein, Aug 07 2017

Status

approved