A163660 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 38, 1406, 52022, 1924814, 71217415, 2635018344, 97494717024, 3607268946840, 133467634460304, 4938253762332042, 182713586854206456, 6760336027236505128, 250129965636431546040, 9254717436709694665512

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170757, 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..635
• Index entries for linear recurrences with constant coefficients, signature (36, 36, 36, 36, -666).

Programs

GAP

a:=[38, 1406, 52022, 1924814, 71217415];; for n in [6..20] do a[n]:=36*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) - 666*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6) )); // G. C. Greubel, Apr 28 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6), {x,0,20}], x] (* G. C. Greubel, Aug 01 2017 *)
coxG[{5, 666, -36}] (* 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)/(1-37*x+702*x^5-666*x^6)) \\ G. C. Greubel, Aug 01 2017

Sage

((1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(666*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).

a(n) = 36*a(n-1)+36*a(n-2)+36*a(n-3)+36*a(n-4)-666*a(n-5). - Wesley Ivan Hurt, May 11 2021