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A147611
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The 3rd Witt transform of A000027.
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1
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0, 0, 0, 0, 2, 7, 18, 42, 84, 153, 264, 429, 666, 1001, 1456, 2061, 2856, 3876, 5166, 6783, 8778, 11214, 14168, 17710, 21924, 26910, 32760, 39582, 47502, 56637, 67122, 79112, 92752, 108207, 125664, 145299, 167310, 191919, 219336, 249795, 283556
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OFFSET
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0,5
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COMMENTS
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a(n) is the number of binary Lyndon words of length n+3 having 3 blocks of 0's, see Math.SE. - Andrey Zabolotskiy, Nov 16 2021
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (4,-6,6,-9,12,-9,6,-6,4,-1).
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FORMULA
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G.f.: x^4*(2-x+2*x^2)/((1-x)^6*(1+x+x^2)^2).
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MATHEMATICA
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CoefficientList[Series[x^4(2 -x+ 2*x^2)/((1-x)^6*(1 +x +x^2)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 13 2012 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 50); [0, 0, 0, 0] cat Coefficients(R!( x^4*(2-x+2*x^2)/((1-x)^6*(1+x+x^2)^2) )); // G. C. Greubel, Oct 24 2022
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x^4*(2-x+2*x^2)/((1-x)^6*(1+x+x^2)^2) ).list()
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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