A163518 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 23, 506, 11132, 244904, 5387635, 118522404, 2607370689, 57359466780, 1261849124844, 27759379635372, 610677728876061, 13434280356535038, 295540315560771435, 6501582206394337062, 143028104664155140584

Offset

0,2

Comments

The initial terms coincide with those of A170742, 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..740

Index entries for linear recurrences with constant coefficients, signature (21, 21, 21, 21, -231).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).

a(n) = 21*a(n-1)+21*a(n-2)+21*a(n-3)+21*a(n-4)-231*a(n-5). - Wesley Ivan Hurt, May 10 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 231, -21}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 16 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6)) \\ G. C. Greubel, Jul 27 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019

Crossrefs

Sequence in context: A162809 A212336 A163171 * A163991 A164636 A164957

Adjacent sequences: A163515 A163516 A163517 * A163519 A163520 A163521

Keyword

nonn,easy

Author

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

Status

approved