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A163552
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Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
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1
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1, 30, 870, 25230, 731670, 21217995, 615309240, 17843602560, 517453877640, 15005855150160, 435160887802830, 12619407316577880, 365955317872798920, 10612486887830912280, 307755817292235608520, 8924735934026717183820
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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 A170749, 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^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(406*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
a(n) = 28*a(n-1)+28*a(n-2)+28*a(n-3)+28*a(n-4)-406*a(n-5). - Wesley Ivan Hurt, May 11 2021
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MATHEMATICA
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CoefficientList[Series[(x^5+2*x^4+2*x^3+2*x^2+2*x+1)/(406*x^5-28*x^4 - 28*x^3-28*x^2-28*x+1), {x, 0, 20}], x] (* Wesley Ivan Hurt, Mar 31 2017 *)
LinearRecurrence[{28, 28, 28, 28, -406}, {1, 30, 870, 25230, 731670, 21217995}, 20] (* Vincenzo Librandi, Apr 01 2017 *)
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PROG
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(Magma) I:=[1, 30, 870, 25230, 731670, 21217995]; [n le 6 select I[n] else 28*Self(n-1)+28*Self(n-2)+28*Self(n-3)+28*Self(n-4)-406*Self(n-5): n in [1..30]]; // Vincenzo Librandi, Apr 01 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-29*x+434*x^5-406*x^6) )); // G. C. Greubel, May 16 2019
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-29*x+434*x^5-406*x^6)) \\ G. C. Greubel, Jul 28 2017
(Sage) ((1+x)*(1-x^5)/(1-29*x+434*x^5-406*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 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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