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

0,2

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).

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

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 *)

Prog

(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
(Magma) R<x>:=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
(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

Crossrefs

Sequence in context: A010559 A342884 A163092 * A163964 A164627 A164867

Adjacent sequences: A163438 A163439 A163440 * A163442 A163443 A163444

Keyword

nonn

Author

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

Status

approved