A163223 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 40, 1560, 60840, 2371980, 92476800, 3605409600, 140564736000, 5480222014020, 213658376756760, 8329936604744040, 324760699264187160, 12661502336823753660, 493636212105145265520, 19245481572342746507280

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170759, 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..625
• Index entries for linear recurrences with constant coefficients, signature (38, 38, 38, -741).

Crossrefs

Cf. A154638, A170759.

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-39*x+779*x^4-741*x^5) )); // G. C. Greubel, Apr 30 2019

Mathematica

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(741*t^4-38*t^3-38*t^2 - 38*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{38, 38, 38, -741}, {1, 40, 1560, 60840, 2371980}, 20] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 741, -38}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 30 2019 *)

PARI

my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(741*t^4- 38*t^3 -38*t^2-38*t+1)) \\ G. C. Greubel, Dec 11 2016

Sage

((1+x)*(1-x^4)/(1-39*x+779*x^4-741*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(741*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).

a(n) = 38*a(n-1)+38*a(n-2)+38*a(n-3)-741*a(n-4). - Wesley Ivan Hurt, May 06 2021