A163835 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 49, 2352, 112896, 5419008, 260111208, 12485281536, 599290805400, 28765828659456, 1380753535666176, 66275870193948072, 3181227392509145280, 152698224757140201048, 7329481664494083280704, 351813529958166317583360

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170768, 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..590
• Index entries for linear recurrences with constant coefficients, signature (47,47,47,47,-1128).

Programs

GAP

a:=[49,2352,112896,5419008,260111208];; for n in [6..20] do a[n]:=47*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -1128*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)/(1-48*t+1175*t^5-1128*t^6) )); // G. C. Greubel, Aug 09 2019

Maple

seq(coeff(series((1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 05 2017 *)
coxG[{5,1128,-47}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 10 2019 *)

PARI

my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6)) \\ G. C. Greubel, Aug 05 2017

Sage

def A163835_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6)).list()
A163835_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)/(1128*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

a(n) = 47*a(n-1)+47*a(n-2)+47*a(n-3)+47*a(n-4)-1128*a(n-5). - Wesley Ivan Hurt, May 11 2021