A163441 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 16, 240, 3600, 54000, 809880, 12146400, 182169120, 2732133600, 40975956000, 614548634280, 9216869130000, 138232634196720, 2073183516810000, 31093163487414000, 466328623499110680, 6993897072666789600

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170735, 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..845
• Index entries for linear recurrences with constant coefficients, signature (14, 14, 14, 14, -105).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6) )); // G. C. Greubel, May 13 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6), {x, 0, 20}], x] (* or *) LinearRecurrence[{14, 14, 14, 14, -105}, {1, 16, 240, 3600, 54000, 809880}, 20] (* G. C. Greubel, Dec 23 2016 *)
coxG[{5, 105, -14}] (* 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)/(1-15*x+119*x^5-105*x^6)) \\ G. C. Greubel, Dec 23 2016

Sage

((1+x)*(1-x^5)/(1-15*x+119*x^5-105*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)/(105*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

a(n) = 14*a(n-1)+14*a(n-2)+14*a(n-3)+14*a(n-4)-105*a(n-5). - Wesley Ivan Hurt, May 10 2021