A362904 Number of nonisomorphic ordered triples of involutions on a (2n)-set that pairwise commute.

1, 8, 43, 176, 611, 1864, 5161, 13184, 31532, 71264, 153444, 316608, 629236, 1209312, 2255324, 4093056, 7246690, 12542736, 21262582, 35359456, 57767766, 92832784, 146908290, 229169792, 352721676, 536076640, 805132548, 1195771840, 1757278132

Offset: 0

Author

Andrew Howroyd, May 11 2023

Keywords

• nonn

Comments

Two involutions x,y commute if x*y = y*x. Isomorphism is up to permutation of the elements of the (2n)-set. a(n) also gives the value for a (2n+1)-set.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8, -21, 0, 106, -176, -70, 512, -435, -392, 1001, -512, -580, 1120, -580, -512, 1001, -392, -435, 512, -70, -176, 106, 0, -21, 8, -1).

Crossrefs

Column k=3 of A362903.

Programs

PARI

C(3,30) \\ C(k,n) defined in A362903.

Formula

G.f.: 1/((1 - x)^16*(1 + x)^8*(1 + x^2)).