A072844 Number of words of length 2n-1 generated by the two letters s and t that reduce to the identity 1 by using the relations sssssss=1, tt=1 and stst=1. The generators s and t along with the three relations generate the 14-element dihedral group D7.

0, 0, 0, 1, 9, 55, 286, 1365, 6188, 27132, 116281, 490337, 2043275, 8439210, 34621041, 141290436, 574274008, 2326683921, 9402807817, 37923176863, 152705590518, 614111175965, 2467123420524, 9903167265124, 39725253489545

Offset

1,5

References

H.S.M. Coxeter and W.O.J. Moser, Generators and Relations for Discrete Groups, Fourth Edition, (p.134).

Links

Table of n, a(n) for n=1..25.

Haggai Liu, Enumerative Properties of Cogrowth Series on Free Products of Finite Groups, ACA 2021 Session on Algorithmic Combinatorics, 2021.

Formula

a(n) = 9*a(n-1) - 26*a(n-2) + 25*a(n-3) - 4*a(n-4).

g.f.: x^4 / ((1 - 4*x)*(1 - 5*x + 6*x^2 - x^3)). - Colin Barker, Feb 24 2017

28*a(n) = 4^n -4*( 2*A005021(n) -9*A005021(n-1) +11*A005021(n-2) ). - R. J. Mathar, Nov 05 2024

Example

The 9 words of length 9 are ssssssstt, sssssstts, sssssttss, ssssttsss, sssttssss, ssttsssss, sttssssss, ttsssssss, tssssssst. - Sean A. Irvine, Oct 31 2024

Crossrefs

Cf. A072266.

Bisection of A377573.

Sequence in context: A016269 A005770 A030053 * A026857 A244650 A097790

Adjacent sequences: A072841 A072842 A072843 * A072845 A072846 A072847

Keyword

nonn

Author

Jamaine Paddyfoot and John W. Layman, Jul 24 2002

Status

approved