A163565 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 32, 992, 30752, 953312, 29552176, 916102080, 28398688320, 880344576960, 27290224296000, 845982768138960, 26225026083540000, 812962177226488800, 25201404928845626400, 781230453493416184800, 24217737986779970583600

Offset

0,2

Comments

The initial terms coincide with those of A170751, 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..665

Index entries for linear recurrences with constant coefficients, signature (30, 30, 30, 30, -465).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(465*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

a(n) = 30*a(n-1)+30*a(n-2)+30*a(n-3)+30*a(n-4)-465*a(n-5). - Wesley Ivan Hurt, May 11 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-31*x+495*x^5-465*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 28 2017 *)
coxG[{5, 465, -30}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 18 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-31*x+495*x^5-465*x^6)) \\ G. C. Greubel, Jul 28 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-31*x+495*x^5-465*x^6) )); // G. C. Greubel, May 18 2019
(SageMath) ((1+x)*(1-x^5)/(1-31*x+495*x^5-465*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 18 2019

Crossrefs

Sequence in context: A228983 A162836 A163215 * A164036 A164668 A165131

Adjacent sequences: A163562 A163563 A163564 * A163566 A163567 A163568

Keyword

nonn

Author

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

Status

approved