A166324 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569138536, 3181328043318593280, 152703746079289769112, 7329779811805778917632, 351829430966671148058624

Offset: 0

Author

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

Keywords

• nonn

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..500
• Index entries for linear recurrences with constant coefficients, signature (47,47,47,47,47,47,47,47,47,-1128).

Programs

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-48*t+1175*t^10-1128*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 12 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-48*t+1175*t^10-1128*t^11), {t,0,30}], t] (* G, C, Greubel, May 09 2016 *)
coxG[{10, 1128, -47}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 12 2020 *)

Sage

def A166324_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-48*t+1175*t^10-1128*t^11) ).list()
A166324_list(30) # G. C. Greubel, Mar 12 2020

Formula

G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1128*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).