A163837 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 50, 2450, 120050, 5882450, 288238825, 14123642400, 692055537600, 33910577282400, 1661611227897600, 81418604280421800, 3989494661371228800, 195484407940615651200, 9578695296400885468800, 469354075590339325411200

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,-1176).

Formula

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

a(n) = 48*a(n-1)+48*a(n-2)+48*a(n-3)+48*a(n-4)-1176*a(n-5). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 05 2017 *)
coxG[{5, 1176, -48}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6)) \\ G. C. Greubel, Aug 05 2017 *)
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6) )); // G. C. Greubel, Aug 09 2019
(Sage)
def A163748_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6)).list()
A163748_list(20) # G. C. Greubel, Aug 09 2019
(GAP) a:=[50, 2450, 120050, 5882450, 288238825];; for n in [6..20] do a[n]:=48*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -1176*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 2019

Crossrefs

Sequence in context: A156087 A162919 A163290 * A164351 A164695 A165182

Adjacent sequences: A163834 A163835 A163836 * A163838 A163839 A163840

Keyword

nonn

Author

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

Status

approved