A163527 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 27, 702, 18252, 474552, 12338001, 320778900, 8340014475, 216834216300, 5637529462500, 146571601954050, 3810753388040625, 99076773337132500, 2575922925294444375, 66972093393463976250, 1741224960366454777500

Offset

0,2

Comments

The initial terms coincide with those of A170746, 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..700

Index entries for linear recurrences with constant coefficients, signature (25, 25, 25, 25, -325).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(325*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).

a(n) = 25*a(n-1)+25*a(n-2)+25*a(n-3)+25*a(n-4)-325*a(n-5). - Wesley Ivan Hurt, May 10 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-26*x+350*x^5-325*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 325, -25}] (* 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)/(1-26*x+350*x^5-325*x^6)) \\ G. C. Greubel, Jul 27 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-26*x+350*x^5-325*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-26*x+350*x^5-325*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019

Crossrefs

Sequence in context: A342037 A162827 A163179 * A164017 A164644 A164969

Adjacent sequences: A163524 A163525 A163526 * A163528 A163529 A163530

Keyword

nonn

Author

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

Status

approved