A166366 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801964, 15818613552, 110730293520, 775112045232, 5425784250768, 37980489294384, 265863421833744, 1861043930247600, 13027307353612944

Offset

0,2

Comments

The initial terms coincide with those of A003950, 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 (6,6,6,6,6,6,6,6,6,6,-21).

Formula

G.f.: (t^11 + 2*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)/(21*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^11)/(1-7*t+27*t^11-21*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 13 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^11)/(1-7*t+27*t^11-21*t^12), {t, 0, 30}], t] (* G. C. Greubel, May 10 2016 *)
coxG[{11, 21, -6}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 13 2020 *)

Prog

(Sage)
def A166366_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^11)/(1-7*t+27*t^11-21*t^12) ).list()
A166366_list(30) # G. C. Greubel, Mar 13 2020

Crossrefs

Sequence in context: A164769 A165215 A165786 * A166538 A166910 A167109

Adjacent sequences: A166363 A166364 A166365 * A166367 A166368 A166369

Keyword

nonn

Author

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

Status

approved