A163503 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 21, 420, 8400, 168000, 3359790, 67191600, 1343748210, 26873288400, 537432252000, 10747974763890, 214946090593500, 4298653734898110, 85967713492846500, 1719247052441058000, 34382796834223386990

Offset

0,2

Comments

The initial terms coincide with those of A170740, 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..765

Index entries for linear recurrences with constant coefficients, signature (19, 19, 19, 19, -190).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

a(n) = 19*a(n-1)+19*a(n-2)+19*a(n-3)+19*a(n-4)-190*a(n-5). - Wesley Ivan Hurt, May 10 2021

Mathematica

coxG[{5, 190, -19}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 09 2015 *)
CoefficientList[Series[(1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 26 2017 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6)) \\ G. C. Greubel, Jul 26 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019

Crossrefs

Sequence in context: A162807 A097833 A163145 * A163977 A164634 A164954

Adjacent sequences: A163500 A163501 A163502 * A163504 A163505 A163506

Keyword

nonn

Author

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

Status

approved