A376313 Independence number of the 2-supertoken graph FF_2(C_n) of the cycle C_n on n vertices.

2, 3, 6, 7, 12, 14, 20, 22, 30, 33, 42, 45, 56, 60, 72, 76, 90, 95, 110, 115, 132, 138, 156, 162, 182, 189, 210, 217, 240, 248, 272, 280, 306, 315, 342, 351, 380, 390, 420, 430, 462, 473, 506, 517, 552, 564, 600, 612, 650, 663, 702, 715, 756, 770, 812, 826, 870, 885, 930, 945, 992, 1008

Offset

2,1

Comments

Given a graph G on n vertices and an integer k>=1, the k-supertoken (or reduced k-th power) FF_k(G) of G has vertices representing configurations of k indistinguishable tokens in the (not necessarily different) vertices of G, with two configurations being adjacent if one can be obtained from the other by moving one token along an edge of G.

Links

Andrew Howroyd, Table of n, a(n) for n = 2..10000

R. H. Hammack and G. D. Smith, Cycle bases of reduced powers of graphs, Ars Math. Contemp. 12 (2017) 183-203.

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

Formula

a(n) = k*(n+2) if n=4*k or n=4*k+1, and a(n)=(k+1)*n if n=4*k+2 or n=4*k+3.

G.f.: x^2*(2 + x + x^2)/((1 - x)^3*(1 + x)^2*(1 + x^2)). - Andrew Howroyd, Nov 13 2025

Prog

(PARI) a(n) = if(bittest(n, 1), n, n+2)*((n+2)\4) \\ Andrew Howroyd, Nov 13 2025

Crossrefs

Sequence in context: A030013 A130404 A362009 * A365411 A064689 A240175

Adjacent sequences: A376310 A376311 A376312 * A376314 A376315 A376316

Keyword

nonn,easy

Author

Miquel A. Fiol, Sep 26 2024

Status

approved