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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, 0, 1, 9, 55, 286, 1365, 6188, 27132, 116281, 490337, 2043275, 8439210, 34621041, 141290436, 574274008, 2326683921, 9402807817, 37923176863, 152705590518, 614111175965, 2467123420524, 9903167265124, 39725253489545 (list; graph; refs; listen; history; text; internal format)
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.

FORMULA

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

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

CROSSREFS

Cf. A072266.

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

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Last modified October 1 11:59 EDT 2020. Contains 337443 sequences. (Running on oeis4.)