A308602 Number of (not necessarily maximal) cliques in the n-cycle graph.

8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133

Offset

3,1

Comments

Also the number of independent vertex sets in the complement of the n-cycle graph. - Eric W. Weisstein, Oct 11 2023

Links

Andrew Howroyd, Table of n, a(n) for n = 3..1000

Eric Weisstein's World of Mathematics, Clique.

Eric Weisstein's World of Mathematics, Cycle Complement Graph.

Eric Weisstein's World of Mathematics, Cycle Graph.

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

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = 2*n+1 for n > 3.

G.f.: x^3*(8 - 7*x + x^2)/(1 - x)^2. - Andrew Howroyd, Nov 06 2025

E.g.f.: exp(x)*(1 + 2*x) - 1 - 3*x - 5*x^2/2 + x^3/6. - Stefano Spezia, Jul 09 2026

Mathematica

Join[{8}, 2*(Range[4, 100]) + 1] (* Paolo Xausa, Jul 09 2026 *)

Crossrefs

Sequence in context: A188056 A128234 A368082 * A087668 A120176 A139049

Adjacent sequences: A308599 A308600 A308601 * A308603 A308604 A308605

Keyword

nonn,easy,changed

Author

Eric W. Weisstein, Jun 09 2019

Status

approved