A163601 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 36, 1260, 44100, 1543500, 54021870, 1890743400, 66175247880, 2316106686600, 81062789409000, 2837164567941270, 99299602743358500, 3475445596778953980, 121639178430430006500, 4257321634653990493500, 149004520868736130568670

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170755, 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..645
• Index entries for linear recurrences with constant coefficients, signature (34, 34, 34, 34, -595).

Programs

GAP

a:=[36, 1260, 44100, 1543500, 54021870];; for n in [6..20] do a[n]:=34*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) - 595*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, May 22 2019

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-35*x+629*x^5-595*x^6) )); // G. C. Greubel, May 22 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-35*x+629*x^5-595*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 29 2017 *)
coxG[{5, 595, -34}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 22 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-35*x+629*x^5-595*x^6)) \\ G. C. Greubel, Jul 29 2017

Sage

((1+x)*(1-x^4)/(1-35*x+629*x^5-595*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 22 2019

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(595*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

a(n) = 34*a(n-1)+34*a(n-2)+34*a(n-3)+34*a(n-4)-595*a(n-5). - Wesley Ivan Hurt, May 11 2021