A163669 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 40, 1560, 60840, 2372760, 92536860, 3608907120, 140746192080, 5489055252720, 214071351558480, 8348712382781940, 325597040159662440, 12698177599143380760, 495224754685478312040, 19313602738540732379160

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, 38, -741).

Programs

GAP

a:=[40, 1560, 60840, 2372760, 92536860];; for n in [6..20] do a[n]:=38*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) -741*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, May 23 2019

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-39*x+779*x^5-741*x^6) )); // G. C. Greubel, May 23 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-39*x+779*x^5-741*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 01 2017 *)
coxG[{5, 741, -38}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 23 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-39*x+779*x^5-741*x^6)) \\ G. C. Greubel, Aug 01 2017

Sage

((1+x)*(1-x^5)/(1-39*x+779*x^5-741*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 23 2019

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(741*t^5 - 38*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)+38*a(n-4)-741*a(n-5). - Wesley Ivan Hurt, May 11 2021