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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
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
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
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved