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A166254
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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.
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1
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1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018888708, 514280812214444, 22114074925220146, 950905221784425600, 40888924536728552592, 1758223755079252588512, 75603621468404628869424
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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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).
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FORMULA
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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).
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Sequence in context: A164688 A165176 A165695 * A166438 A166723 A167097
Adjacent sequences: A166251 A166252 A166253 * A166255 A166256 A166257
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KEYWORD
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nonn
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AUTHOR
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John Cannon and N. J. A. Sloane, Dec 03 2009
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STATUS
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approved
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