A163397 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 10, 90, 810, 7290, 65565, 589680, 5303520, 47699280, 429001920, 3858394860, 34701968160, 312105587040, 2807042441760, 25246223065440, 227061682284240, 2042167156174080, 18367021030590720, 165190915209012480

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, 8, -36).

Programs

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6) )); // G. C. Greubel, May 12 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{8,8,8,8,-36}, {1,10,90,810,7290,65565}, 30] (* G. C. Greubel, Dec 21 2016 *)
coxG[{5, 36, -8}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)

PARI

my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6)) \\ G. C. Greubel, Dec 21 2016

Sage

((1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

a(n) = 8*a(n-1)+8*a(n-2)+8*a(n-3)+8*a(n-4)-36*a(n-5). - Wesley Ivan Hurt, May 10 2021