A163440 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 15, 210, 2940, 41160, 576135, 8064420, 112881405, 1580053020, 22116729180, 309578036040, 4333306233165, 60655281460410, 849019887139515, 11884122064943310, 166347525415813560, 2328442863574420320

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..855
• Index entries for linear recurrences with constant coefficients, signature (13, 13, 13, 13, -91).

Programs

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6) )); // G. C. Greubel, May 12 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{13, 13, 13, 13, -91}, {15, 210, 2940, 41160, 576135}, 30] (* G. C. Greubel, Dec 23 2016 *)
coxG[{5, 91, -13}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)

PARI

my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6)) \\ G. C. Greubel, Dec 23 2016

Sage

((1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

Formula

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

a(n) = 13*a(n-1)+13*a(n-2)+13*a(n-3)+13*a(n-4)-91*a(n-5). - Wesley Ivan Hurt, May 10 2021