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A166313
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Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
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1
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1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708931688, 2524758347319736320, 118663642324025116416, 5577191189229063412224, 262127985893760478586112
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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 A170767, 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 (46,46,46,46,46,46,46,46,46,-1081).
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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)/(1081*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
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MAPLE
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seq(coeff(series((1+t)*(1-t^10)/(1-47*t+1127*t^10-1081*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)/(1-47*t+1127*t^10-1081*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{10, 1081, -46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 05 2017 *)
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PROG
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(Sage)
def A166313_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-47*t+1127*t^10-1081*t^11) ).list()
A166313_list(30) # G. C. Greubel, Mar 11 2020
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CROSSREFS
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Sequence in context: A164693 A165180 A165708 * A166442 A166854 A167101
Adjacent sequences: A166310 A166311 A166312 * A166314 A166315 A166316
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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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