A287327 Number of independent vertex sets (and vertex covers) in the 2n-crossed prism graph.

2, 7, 35, 196, 1127, 6517, 37730, 218491, 1265327, 7327852, 42437675, 245768761, 1423317602, 8242841887, 47736669995, 276456796756, 1601040887327, 9272088633997, 53697334226690, 310976719148851, 1800955694455127, 10429852827143932, 60402279928821635

Offset: 0

Author

Andrew Howroyd, Aug 31 2017

Keywords

• nonn

Comments

Sequence extrapolated to n = 0 using recurrence.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• Eric Weisstein's World of Mathematics, Crossed Prism Graph
• Eric Weisstein's World of Mathematics, Independent Vertex Set
• Eric Weisstein's World of Mathematics, Vertex Cover
• Index entries for linear recurrences with constant coefficients, signature (7, -7).

Crossrefs

Cf. A276225 (maximal independent vertex sets), A287062, A290708.

Programs

Mathematica

CoefficientList[Series[(2 - 7 x)/(1 - 7 x + 7 x^2), {x, 0, 22}], x] (* Michael De Vlieger, Aug 31 2017 *)
Table[(1/2 (7 - Sqrt[21]))^n + (1/2 (7 + Sqrt[21]))^n, {n, 0, 20}] // Expand (* Eric W. Weisstein, Sep 21 2017 *)
LinearRecurrence[{7, -7}, {7, 35}, {0, 20}] (* Eric W. Weisstein, Sep 21 2017 *)

PARI

Vec((2 - 7*x)/(1 - 7*x + 7*x^2) + O(x^30))

Formula

a(n) = 7*a(n-1) - 7*a(n-2) for n > 1.

G.f.: (2 - 7*x)/(1 - 7*x + 7*x^2).