A162889 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 46, 2070, 92115, 4098600, 182342160, 8112199590, 360902223000, 16056115855560, 714317717862540, 31779155482826400, 1413817266133308960, 62899068010426041240, 2798305588240613272800, 124493325781573753947360

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..605
• Index entries for linear recurrences with constant coefficients, signature (44, 44, -990).

Programs

GAP

a:=[46,2070,92115];; for n in [4..20] do a[n]:=44*a[n-1]+44*a[n-2] - 990*a[n-3]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(990*t^3-44*t^2-44*t+1))); // G. C. Greubel, Oct 24 2018

Mathematica

CoefficientList[Series[(t^3+2*t^2+2*t+1)/(990*t^3-44*t^2-44*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)
coxG[{3, 990, -44}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *)

PARI

my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(990*t^3-44*t^2-44*t+1)) \\ G. C. Greubel, Oct 24 2018

Sage

((1+x)*(1-x^3)/(1-45*x+1034*x^3-990*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019

Formula

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

From G. C. Greubel, Apr 28 2019: (Start)

a(n) = 44*a(n-1) + 44*a(n-2) - 990*a(n-3).

G.f.: (1+x)*(1-x^3)/(1 - 45*x + 1034*x^3 - 990*x^4). (End)