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A162755
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Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
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0
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1, 9, 72, 540, 4032, 29988, 223020, 1658160, 12328596, 91662732, 681510816, 5067014148, 37673118252, 280098623952, 2082525799284, 15483523651596, 115119584685504, 855911035979748, 6363675682412076, 47313758657548656
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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 A003951, 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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FORMULA
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G.f.: (t^3 + 2*t^2 + 2*t + 1)/(28*t^3 - 7*t^2 - 7*t + 1)
a(0)=1, a(1)=9, a(2)=72, a(3)=540, a(n)=7*a(n-1)+7*a(n-2)-28*a(n-3). - Harvey P. Dale, Jun 15 2011
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MATHEMATICA
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Join[{1}, LinearRecurrence[{7, 7, -28}, {9, 72, 540}, 50]] (* or *) CoefficientList[ Series[(t^3+2t^2+2t+1)/(28t^3-7t^2-7t+1), {t, 0, 50}], t] (* Harvey P. Dale, Jun 15 2011 *)
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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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