A163451 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 17, 272, 4352, 69632, 1113976, 17821440, 285108360, 4561178880, 72969984000, 1167377713080, 18675771192000, 298775988016200, 4779834262113600, 76468044587443200, 1223339873805905400, 19571056837109136000

Offset

0,2

Comments

The initial terms coincide with those of A170736, 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..825

Index entries for linear recurrences with constant coefficients, signature (15, 15, 15, 15, -120).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(120*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).

a(n) = 15*a(n-1)+15*a(n-2)+15*a(n-3)+15*a(n-4)-120*a(n-5). - Wesley Ivan Hurt, May 10 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-16*x+135*x^5-120*x^6), {x, 0, 20}], x] (* G. C. Greubel, Dec 24 2016 *)
coxG[{5, 120, -15}] (* 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)/(1-16*x+135*x^5-120*x^6)) \\ G. C. Greubel, Dec 24 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-16*x+135*x^5-120*x^6) )); // G. C. Greubel, May 13 2019
(Sage) ((1+x)*(1-x^5)/(1-16*x+135*x^5-120*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 13 2019

Crossrefs

Sequence in context: A162803 A097830 A163093 * A163965 A164628 A164868

Adjacent sequences: A163448 A163449 A163450 * A163452 A163453 A163454

Keyword

nonn

Author

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

Status

approved