A163454 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 20, 380, 7220, 137180, 2606230, 49514760, 940712040, 17872229160, 339547661640, 6450936451470, 122558879953620, 2328449391567180, 44237321450224020, 840447989197392780, 15967350630411275430

Offset

0,2

Comments

The initial terms coincide with those of A170739, 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..750

Index entries for linear recurrences with constant coefficients, signature (18, 18, 18, 18, -171).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).

a(n) = 18*a(n-1)+18*a(n-2)+18*a(n-3)+18*a(n-4)-171*a(n-5). - Wesley Ivan Hurt, May 10 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6), {x, 0, 20}], x] (* or *) LinearRecurrence[{18, 18, 18, 18, -171}, {1, 20, 380, 7220, 137180, 2606230}, 20] (* G. C. Greubel, Dec 24 2016 *)
coxG[{5, 171, -18}] (* 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)/(1-19*x+189*x^5-171*x^6)) \\ G. C. Greubel, Dec 24 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6) )); // G. C. Greubel, May 13 2019
(Sage) ((1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 13 2019

Crossrefs

Sequence in context: A097832 A342886 A163124 * A163969 A164633 A164911

Adjacent sequences: A163451 A163452 A163453 * A163455 A163456 A163457

Keyword

nonn

Author

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

Status

approved