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A166420
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Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
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1
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1, 26, 650, 16250, 406250, 10156250, 253906250, 6347656250, 158691406250, 3967285156250, 99182128906250, 2479553222655925, 61988830566390000, 1549720764159547200, 38743019103983610000, 968575477599463500000
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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 A170745, 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 (24,24,24,24,24,24,24,24,24,24,-300).
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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)/(300*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).
a(n) = 24*Sum_{j=1..10} a(n-j) - 300*a(n-11).
G.f.: (1+x)*(1-x^11)/(1 - 25*x + 324*x^11 - 300*x^12). (End)
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MATHEMATICA
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With[{p=300, q=24}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(q+1)*t + (p+q)*t^11-p*t^12), {t, 0, 40}], t]] (* G. C. Greubel, May 13 2016; Jul 25 2024 *)
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PROG
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(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-25*x+324*x^11-300*x^12) )); // G. C. Greubel, Jul 25 2024
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^11)/(1-25*x+324*x^11-300*x^12) ).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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