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A163207
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Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
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1
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1, 29, 812, 22736, 636202, 17802288, 498146166, 13939191504, 390048294510, 10914382803996, 305407698579522, 8545958486918244, 239134137088822794, 6691482951706744632, 187241958166564053774, 5239429159586654676168
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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 A170748, 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^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(378*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
a(n) = 27*(a(n-1) + a(n-2) + a(n-3) -14*a(n-4)).
G.f.: (1+x)*(1-x^4)/(1 - 28*x + 405*x^4 - 378*x^5). (End)
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MATHEMATICA
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CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(378*t^4-27*t^3-27*t^2 - 27*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{27, 27, 27, -378}, {1, 29, 812, 22736, 636202}, 20] (* G. C. Greubel, Dec 10 2016 *)
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PROG
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(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5)) \\ G. C. Greubel, Dec 10 2016, modified Apr 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[29, 812, 22736, 636202];; for n in [5..20] do a[n]:=27*(a[n-1] +a[n-2]+a[n-3] -14*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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