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A166328
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Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
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1
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1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236190, 708552, 2125608, 6376680, 19129608, 57387528, 172158696, 516464424, 1549358280, 4647969864, 13943594664, 41829839238, 125486683524, 376451548188, 1129329137988
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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 A003946, 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..1000
Index entries for linear recurrences with constant coefficients, signature (2,2,2,2,2,2,2,2,2,2,-3).
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FORMULA
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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)/(3*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).
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MAPLE
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seq(coeff(series((1+t)*(1-t^11)/(1-3*t+5*t^11-3*t^12), t, n+1), t, n), n = 0..30); # G. C. Greubel, Mar 12 2020
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MATHEMATICA
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CoefficientList[Series[(1+t)*(1-t^11)/(1-3*t+5*t^11-3*t^12), {t, 0, 30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{11, 3, -2}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 12 2020 *)
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PROG
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(Sage)
def A166328_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^11)/(1-3*t+5*t^11-3*t^12) ).list()
A166328_list(30) # G. C. Greubel, Aug 10 2019
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CROSSREFS
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Sequence in context: A164697 A165184 A165756 * A166468 A166858 A167105
Adjacent sequences: A166325 A166326 A166327 * A166329 A166330 A166331
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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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