A163232 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 46, 2070, 93150, 4190715, 188535600, 8482007160, 381596054400, 17167581467190, 772350369021000, 34747182860785560, 1563237055602189000, 70328294002955286540, 3163991615757072698400, 142344458748855549948960

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, -990).

Programs

GAP

a:=[46,2070,93150,4190715];; for n in [5..20] do a[n]:=44*(a[n-1] +a[n-2] +a[n-3]) -990*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, May 01 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^4)/(1-45*x+1034*x^4-990*x^5) )); // G. C. Greubel, May 01 2019

Mathematica

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(990*t^4-44*t^3-44*t^2 - 44*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {44, 44, 44, -990}, {46,2070,93150,4190715}, 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 990, -44}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 01 2019 *)

PARI

my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(990*t^4-44*t^3 - 44*t^2-44*t+1)) \\ G. C. Greubel, Dec 11 2016

Sage

((1+x)*(1-x^4)/(1-45*x+1034*x^4-990*x^5)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(990*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)-990*a(n-4). - Wesley Ivan Hurt, May 10 2021