A164351 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 50, 2450, 120050, 5882450, 288240050, 14123761225, 692064240000, 33911144820000, 1661645952120000, 81420644594940000, 3989611239264000000, 195490933775422559400, 9579054924518618851200, 469373650608038610268800

Offset

0,2

Comments

The initial terms coincide with those of A170769, 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..590

Index entries for linear recurrences with constant coefficients, signature (48, 48, 48, 48, 48, -1176).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1176*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).

a(n) = -1176*a(n-6) + 48*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^6)/(1-49*t+1224*t^6-1176*t^7), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 24 2019

Mathematica

coxG[{6, 1176, -48}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 18 2015 *)
CoefficientList[Series[(1+t)*(1-t^6)/(1-49*t+1224*t^6-1176*t^7), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2017 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^6)/(1-49*t+1224*t^6-1176*t^7)) \\ G. C. Greubel, Sep 15 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^6)/(1-49*t+1224*t^6-1176*t^7) )); // G. C. Greubel, Aug 24 2019
(Sage)
def A164351_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-49*t+1224*t^6-1176*t^7)).list()
A164351_list(20) # G. C. Greubel, Aug 24 2019
(GAP) a:=[50, 2450, 120050, 5882450, 288240050, 14123761225];; for n in [7..20] do a[n]:=48*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -1176*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 24 2019

Crossrefs

Sequence in context: A162919 A163290 A163837 * A164695 A165182 A165726

Adjacent sequences: A164348 A164349 A164350 * A164352 A164353 A164354

Keyword

nonn

Author

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

Status

approved