A164331 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 46, 2070, 93150, 4191750, 188628750, 8488292715, 381973125600, 17188788557160, 773495390804400, 34807288344147000, 1566327784594320000, 70484741716592195190, 3171812990689846701000, 142731567185989127785560

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 (44,44,44,44,44,-990).

Programs

GAP

a:=[46, 2070, 93150, 4191750, 188628750, 8488292715];; for n in [7..30] do a[n]:=44*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -990*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 16 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-45*t+1034*t^6-990*t^7) )); // G. C. Greubel, Aug 16 2019

Maple

seq(coeff(series((1+t)*(1-t^6)/(1-45*t+1034*t^6-990*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 16 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^6)/(1-45*t+1034*t^6-990*t^7), {t,0,30}], t] (* G. C. Greubel, Sep 14 2017 *)
coxG[{6, 990, -44}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 16 2019 *)

PARI

my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-45*t+1034*t^6-990*t^7)) \\ G. C. Greubel, Sep 14 2017

Sage

def A164331_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-45*t+1034*t^6-990*t^7)).list()
A164331_list(30) # G. C. Greubel, Aug 16 2019

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(990*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).

a(n) = -990*a(n-6) + 44*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021