A163565 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 32, 992, 30752, 953312, 29552176, 916102080, 28398688320, 880344576960, 27290224296000, 845982768138960, 26225026083540000, 812962177226488800, 25201404928845626400, 781230453493416184800, 24217737986779970583600

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170751, 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..665
• Index entries for linear recurrences with constant coefficients, signature (30, 30, 30, 30, -465).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-31*x+495*x^5-465*x^6) )); // G. C. Greubel, May 18 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-31*x+495*x^5-465*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 28 2017 *)
coxG[{5, 465, -30}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 18 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-31*x+495*x^5-465*x^6)) \\ G. C. Greubel, Jul 28 2017

Sage

((1+x)*(1-x^5)/(1-31*x+495*x^5-465*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 18 2019

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(465*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

a(n) = 30*a(n-1)+30*a(n-2)+30*a(n-3)+30*a(n-4)-465*a(n-5). - Wesley Ivan Hurt, May 11 2021