A163802 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 46, 2070, 93150, 4191750, 188627715, 8488200600, 381966932160, 17188417679400, 773474553522000, 34806164017265190, 1566268790718951000, 70481709031863535560, 3171659511757241439000, 142723895272921025613000

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170765, 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..600
• Index entries for linear recurrences with constant coefficients, signature (44,44,44,44,-990).

Programs

GAP

a:=[46, 2070, 93150, 4191750, 188627715];; for n in [6..30] do a[n]:=44*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -990*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 2019

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6) )); // G. C. Greubel, Aug 09 2019

Maple

seq(coeff(series((1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 04 2017 *)
coxG[{5, 990, -44}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 09 2019 *)

PARI

my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6)) \\ G. C. Greubel, Aug 04 2017

Sage

def A163802_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6)).list()
A163802_list(20) # G. C. Greubel, Aug 09 2019

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(990*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).

a(n) = 44*a(n-1)+44*a(n-2)+44*a(n-3)+44*a(n-4)-990*a(n-5). - Wesley Ivan Hurt, May 11 2021