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

Author

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

Keywords

• nonn

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).

Programs

Magma

R:=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

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 *)

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

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

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