A163438 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 13, 156, 1872, 22464, 269490, 3232944, 38784174, 465276240, 5581708704, 66961236342, 803303685756, 9636871221978, 115609188148740, 1386911174446512, 16638146470934274, 199600322709006648

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

The initial terms coincide with those of A170732, 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..920
• Index entries for linear recurrences with constant coefficients, signature (11,11,11,11,-66).

Programs

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-12*x+77*x^5-66*x^6) )); // G. C. Greubel, May 12 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-12*x+77*x^5-66*x^6), {x, 0, 10}], x] (* or *) LinearRecurrence[{11, 11, 11, 11, -66}, {1, 13, 156, 1872, 22464, 269490}, 30] (* G. C. Greubel, Dec 23 2016 *)
coxG[{5, 66, -11}] (* 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)/(1-12*x+77*x^5-66*x^6)) \\ G. C. Greubel, Dec 23 2016

Sage

((1+x)*(1-x^5)/(1-12*x+77*x^5-66*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)/(66*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).

a(n) = 11*a(n-1)+11*a(n-2)+11*a(n-3)+11*a(n-4)-66*a(n-5). - Wesley Ivan Hurt, May 10 2021