A164330 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 45, 1980, 87120, 3833280, 168664320, 7421229090, 326534036400, 14367495685950, 632169725893200, 27815464230602400, 1223880262963776000, 53850724390367020710, 2369431557254469630780, 104254974618644628784170

Offset

0,2

Comments

The initial terms coincide with those of A170764, 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..600

Index entries for linear recurrences with constant coefficients, signature (43, 43, 43, 43, 43, -946).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).

G.f.: (1+x)*(1-x^6)/(1 -44*x +989*x^6 -946*x^7). - G. C. Greubel, Apr 25 2019

a(n) = -946*a(n-6) + 43*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 06 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7), {x, 0, 20}], x] (* G. C. Greubel, Sep 14 2017, modified Apr 25 2019 *)
coxG[{6, 946, -43}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 25 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7)) \\ G. C. Greubel, Sep 14 2017, modified Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

Crossrefs

Sequence in context: A162885 A163231 A163749 * A164690 A165177 A165699

Adjacent sequences: A164327 A164328 A164329 * A164331 A164332 A164333

Keyword

nonn

Author

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

Status

approved