A007986 Co-growth function of the symmetric group S_3 generated by 6 generators together with their inverses, with the relations sending each generator to a different element of the group (counting only reduced words).

2, 12, 242, 2772, 29282, 320892, 3543122, 38987652, 428717762, 4715748972, 51874849202, 570624951732, 6276856753442, 69045406572252, 759499667166482, 8354496533703012, 91899459727144322, 1010894054854998732, 11119834626984462962

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..960

Stephen P Humphries, Cogrowth of groups and the Dedekind-Frobenius group determinant, Mathematical Proceeding Cambridge Philosophical Society, volume 121 Part 2, pages 193-217 (1997).

Index entries for linear recurrences with constant coefficients, signature (11,-11,121).

Formula

a(n) = 2 * 11^(n-1) + (-1)^(n/2) * 5 * 11^(n/2-1) * (cos(Pi*n) + 1) [from Humphries]. Sean A. Irvine, Feb 26 2018

a(n)= +11*a(n-1) -11*a(n-2) +121*a(n-3). - R. J. Mathar, Aug 15 2025

G.f.: -2*x*(1-5*x+66*x^2) / ( (11*x-1)*(11*x^2+1) ). - R. J. Mathar, Aug 15 2025

Mathematica

LinearRecurrence[{11, -11, 121}, {2, 12, 242}, 25] (* Paolo Xausa, May 05 2026 *)

Crossrefs

Sequence in context: A087046 A111403 A325501 * A013503 A231074 A132481

Adjacent sequences: A007983 A007984 A007985 * A007987 A007988 A007989

Keyword

nonn,easy

Author

Stephen P. Humphries

Extensions

More terms from Sean A. Irvine, Feb 26 2018

Name clarified by Andrei Zabolotskii, Apr 29 2026

Status

approved