A163317 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 6, 30, 150, 750, 3735, 18600, 92640, 461400, 2298000, 11445210, 57003000, 283904040, 1413987000, 7042377000, 35074632060, 174689570400, 870043225440, 4333259349600, 21581843340000, 107488595621160, 535348070440800

Offset

0,2

Comments

The initial terms coincide with those of A003948, 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..1000

Index entries for linear recurrences with constant coefficients, signature (4, 4, 4, 4, -10).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(10*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).

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

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-5*x+14*x^5-10*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{4, 4, 4, 4, -10}, {1, 6, 30, 150, 750, 3735}, 30] (* G. C. Greubel, Dec 18 2016 *)
coxG[{5, 10, -4}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-5*x+14*x^5-10*x^6)) \\ G. C. Greubel, Dec 18 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-5*x+14*x^5-10*x^6) )); // G. C. Greubel, May 12 2019
(Sage) ((1+x)*(1-x^5)/(1-5*x+14*x^5-10*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

Crossrefs

Sequence in context: A162937 A006818 A006819 * A342807 A163922 A164365

Adjacent sequences: A163314 A163315 A163316 * A163318 A163319 A163320

Keyword

nonn

Author

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

Status

approved