A376313 - OEIS

%I #22 Nov 13 2025 13:43:09

%S 2,3,6,7,12,14,20,22,30,33,42,45,56,60,72,76,90,95,110,115,132,138,

%T 156,162,182,189,210,217,240,248,272,280,306,315,342,351,380,390,420,

%U 430,462,473,506,517,552,564,600,612,650,663,702,715,756,770,812,826,870,885,930,945,992,1008

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

%C 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.

%H Andrew Howroyd, <a href="/A376313/b376313.txt">Table of n, a(n) for n = 2..10000</a>

%H R. H. Hammack and G. D. Smith, <a href="https://doi.org/10.26493/1855-3974.856.4d2">Cycle bases of reduced powers of graphs</a>, Ars Math. Contemp. 12 (2017) 183-203.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1,-1,-1,1).

%F 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.

%F G.f.: x^2*(2 + x + x^2)/((1 - x)^3*(1 + x)^2*(1 + x^2)). - _Andrew Howroyd_, Nov 13 2025

%o (PARI) a(n) = if(bittest(n,1), n, n+2)*((n+2)\4) \\ _Andrew Howroyd_, Nov 13 2025

%K nonn,easy

%O 2,1

%A _Miquel A. Fiol_, Sep 26 2024