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

0,2

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..500

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

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).

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 *)

Prog

(Sage)
def A166324_list(prec):
    P.<t> = 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

Crossrefs

Sequence in context: A164694 A165181 A165709 * A166443 A166855 A167102

Adjacent sequences: A166321 A166322 A166323 * A166325 A166326 A166327

Keyword

nonn

Author

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

Status

approved