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A163287
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Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
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1
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1, 49, 2352, 112896, 5417832, 259999488, 12477267096, 598778820864, 28735144795560, 1378987562102976, 66177035471527512, 3175808211876089664, 152405705797427455464, 7313885981134376257152, 350990324575741067673624
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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 A170768, 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)/(1128*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
a(n) = 47*a(n-1)+47*a(n-2)+47*a(n-3)-1128*a(n-4). - Wesley Ivan Hurt, May 10 2021
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MATHEMATICA
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CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(1128*t^4-47*t^3-47*t^2 - 47*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{47, 47, 47, -1128}, {1, 49, 2352, 112896, 5417832}, 20] (* G. C. Greubel, Dec 17 2016 *)
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PROG
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(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(1128*t^4-47*t^3 - 47*t^2-47*t+1)) \\ G. C. Greubel, Dec 17 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-48*x+1175*x^4-1128*x^5) )); // G. C. Greubel, May 01 2019
(Sage) ((1+x)*(1-x^4)/(1-48*x+1175*x^4-1128*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019
(GAP) a:=[49, 2352, 112896, 5417832];; for n in [5..20] do a[n]:=47*(a[n-1]+a[n-2] +a[n-3] -24*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, May 01 2019
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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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