A166254 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018888708, 514280812214444, 22114074925220146, 950905221784425600, 40888924536728552592, 1758223755079252588512, 75603621468404628869424

Offset

0,2

Comments

The initial terms coincide with those of A170763, 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 (42, 42, 42, 42, 42, 42, 42, 42, 42, -903).

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)/(903*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-43*t+945*t^10-903*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-43*t+945*t^10-903*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 08 2016 *)
coxG[{10, 903, -42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 18 2018 *)

Prog

(Sage)
def A166254_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-43*t+945*t^10-903*t^11) ).list()
A166254_list(30) # G. C. Greubel, Aug 10 2019

Crossrefs

Sequence in context: A164688 A165176 A165695 * A166438 A166723 A167097

Adjacent sequences: A166251 A166252 A166253 * A166255 A166256 A166257

Keyword

nonn

Author

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

Status

approved