A163677 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 41, 1640, 65600, 2624000, 104959180, 4198334400, 167932064820, 6717230145600, 268687107936000, 10747400402591580, 429892659535950000, 17195572119777744420, 687817514366631090000, 27512485759363357584000

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170760, 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..620
• Index entries for linear recurrences with constant coefficients, signature (39, 39, 39, 39, -780).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-40*x+819*x^5-780*x^6) )); // G. C. Greubel, May 24 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-40*x+819*x^5-780*x^6), {x,0,20}], x] (* G. C. Greubel, Aug 02 2017 *)
coxG[{5, 780, -39}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 24 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-40*x+819*x^5-780*x^6)) \\ G. C. Greubel, Aug 02 2017

Sage

((1+x)*(1-x^5)/(1-40*x+819*x^5-780*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 24 2019

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).

a(n) = 39*a(n-1)+39*a(n-2)+39*a(n-3)+39*a(n-4)-780*a(n-5). - Wesley Ivan Hurt, May 11 2021