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A166167
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Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
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1
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1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540946432, 2899474071552, 104381066575872, 3757718396730726, 135277862282282160, 4870003042161295290, 175320109517775581520, 6311523942638803173600
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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 A170756, 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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Index entries for linear recurrences with constant coefficients, signature (35,35,35,35,35,35,35,35,35,-630).
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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)/(630*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).
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MAPLE
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seq(coeff(series((1+t)*(1-t^10)/(1-36*t+665*t^10-630*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)/(1-36*t+665*t^10-630*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 06 2016 *)
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PROG
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(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-36*t+665*t^10-630*t^11) ).list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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