A007985 Co-growth function of a certain group.

2, 2, 6, 22, 58, 146, 414, 1206, 3410, 9634, 27670, 79926, 230666, 667058, 1936174, 5632662, 16408866, 47875650, 139908774, 409404630, 1199368026, 3517351890, 10325547582, 30339113718, 89217594738, 262561101282, 773248631222, 2278737199606

Offset: 1

Author

Stephen P. Humphries

Keywords

• nonn

Links

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

Formula

G.f. (x+1) * sqrt(1-x) / sqrt((1-3*x) * (3*x^2+1)) [from Humphries]. - Sean A. Irvine, Feb 26 2018

D-finite with recurrence n*a(n) +(-3*n+1)*a(n-1) +2*(n+1)*a(n-2) -6*n*a(n-3) +3*(-n+6)*a(n-4) +9*(n-5)*a(n-5)=0. - R. J. Mathar, Aug 15 2025

Extensions

More terms from Sean A. Irvine, Feb 26 2018