A163593 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 34, 1122, 37026, 1221858, 40320753, 1330566336, 43908078720, 1448946455616, 47814568344576, 1577858820890352, 52068617261591040, 1718240483647446528, 56701147733816154624, 1871111864101388705280, 61745833160498214613248

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170753, 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..655
• Index entries for linear recurrences with constant coefficients, signature (32, 32, 32, 32, -528).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6) )); // G. C. Greubel, Apr 28 2019

Mathematica

coxG[{5,528,-32}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 04 2016 *)
CoefficientList[Series[(1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 29 2017 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6)) \\ G. C. Greubel, Jul 29 2017

Sage

((1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).

a(n) = 32*a(n-1)+32*a(n-2)+32*a(n-3)+32*a(n-4)-528*a(n-5). - Wesley Ivan Hurt, May 11 2021