A163452 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 18, 306, 5202, 88434, 1503225, 25552224, 434343744, 7383094560, 125499873024, 2133281378232, 36262103930496, 616393221671808, 10477621608796800, 178101495469706112, 3027418232198243904, 51460888233840150528

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170737, 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..800
• Index entries for linear recurrences with constant coefficients, signature (16, 16, 16, 16, -136).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6) )); // G. C. Greubel, May 13 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6), {x, 0, 20}], x] (* or *)  LinearRecurrence[{16,16,16,16,-136}, {1, 18, 306, 5202, 88434, 1503225}, 20] (* G. C. Greubel, Dec 24 2016 *)
coxG[{5, 136, -16}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 13 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6)) \\ G. C. Greubel, Dec 24 2016

Sage

((1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 13 2019

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).

a(n) = 16*a(n-1)+16*a(n-2)+16*a(n-3)+16*a(n-4)-136*a(n-5). - Wesley Ivan Hurt, May 10 2021