A162983 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 10, 90, 810, 7245, 64800, 579600, 5184000, 46366380, 414707040, 3709193760, 33175513440, 296726124240, 2653957198080, 23737339710720, 212309865780480, 1898927161041600, 16984252473131520, 151909371770042880

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003952, 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..1000
• Index entries for linear recurrences with constant coefficients, signature (8, 8, 8, -36).

Programs

GAP

a:=[10,90,810,7245];; for n in [5..20] do a[n]:=8*(a[n-1]+a[n-2] +a[n-3]) - 36*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5) )); // G. C. Greubel, Apr 28 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5), {x,0,20}], x]
(* or *) coxG[{4, 36, -8}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5)) \\ G. C. Greubel, Apr 28 2019

Sage

((1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

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

a(n) = 8*(a(n-1) + a(n-2) + a(n-3)) - 36*a(n-4).

G.f.: (1+x)*(1-x^4)/(1 - 9*x + 44*x^4 - 36*x^5). (End)