A163526 - OEIS

A163526

Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 26, 650, 16250, 406250, 10155925, 253890000, 6347047200, 158671110000, 3966651000000, 99163106355300, 2478998445300000, 61972980856207200, 1549275016079700000, 38730637808401500000, 968235006358878382800

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170745, 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..710

Index entries for linear recurrences with constant coefficients, signature (24, 24, 24, 24, -300).

FORMULA

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).

a(n) = 24*a(n-1)+24*a(n-2)+24*a(n-3)+24*a(n-4)-300*a(n-5). - Wesley Ivan Hurt, May 10 2021

MATHEMATICA

CoefficientList[Series[(1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)

coxG[{5, 300, -24}] (* 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)/(1-25*x+324*x^5-300*x^6)) \\ G. C. Greubel, Jul 27 2017

(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6) )); // G. C. Greubel, May 16 2019

(Sage) ((1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019

CROSSREFS

Sequence in context: A106793 A162812 A163177 * A163995 A164639 A164964

Adjacent sequences: A163523 A163524 A163525 * A163527 A163528 A163529

KEYWORD

nonn

AUTHOR

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

STATUS

approved