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

0,1

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).

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).

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 *)

Prog

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

Crossrefs

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

Sequence in context: A182408 A057298 A058941 * A020066 A024719 A086637

Adjacent sequences: A287324 A287325 A287326 * A287328 A287329 A287330

Keyword

nonn

Author

Andrew Howroyd, Aug 31 2017

Status

approved