A163962 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 15, 210, 2940, 41160, 576240, 8067255, 112940100, 1581140925, 22135686300, 309895595100, 4338482148000, 60737963515320, 850320477564285, 11904332524792890, 166658497119549435, 2333188744879254990

Offset

0,2

Comments

The initial terms coincide with those of A170734, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

G. C. Greubel, Table of n, a(n) for n = 0..870

Index entries for linear recurrences with constant coefficients, signature (13, 13, 13, 13, 13, -91).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(91*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).

G.f.: (1+x)*(1-x^6)/(1 -14*x +104*x^6 -91*x^7). - G. C. Greubel, Apr 25 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^6)/(1-14*x+104*x^6-91*x^7), {x, 0, 20}], x] (* G. C. Greubel, Aug 13 2017, modified Apr 25 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-14*x+104*x^6-91*x^7)) \\ G. C. Greubel, Aug 13 2017, modified Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-14*x+104*x^6-91*x^7) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^6)/(1-14*x+104*x^6-91*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

Crossrefs

Sequence in context: A076139 A163091 A163440 * A164626 A164860 A165282

Adjacent sequences: A163959 A163960 A163961 * A163963 A163964 A163965

Keyword

nonn

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Status

approved