A163835 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 49, 2352, 112896, 5419008, 260111208, 12485281536, 599290805400, 28765828659456, 1380753535666176, 66275870193948072, 3181227392509145280, 152698224757140201048, 7329481664494083280704, 351813529958166317583360

Offset

0,2

Comments

The initial terms coincide with those of A170768, 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 (47,47,47,47,-1128).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1128*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

a(n) = 47*a(n-1)+47*a(n-2)+47*a(n-3)+47*a(n-4)-1128*a(n-5). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 05 2017 *)
coxG[{5, 1128, -47}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 10 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6)) \\ G. C. Greubel, Aug 05 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6) )); // G. C. Greubel, Aug 09 2019
(Sage)
def A163835_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6)).list()
A163835_list(20) # G. C. Greubel, Aug 09 2019
(GAP) a:=[49, 2352, 112896, 5419008, 260111208];; for n in [6..20] do a[n]:=47*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -1128*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 2019

Crossrefs

Sequence in context: A049682 A162914 A163287 * A164350 A164694 A165181

Adjacent sequences: A163832 A163833 A163834 * A163836 A163837 A163838

Keyword

nonn

Author

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

Status

approved