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A239632
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Number of parts in all palindromic compositions of n.
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2
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0, 1, 3, 4, 10, 12, 28, 32, 72, 80, 176, 192, 416, 448, 960, 1024, 2176, 2304, 4864, 5120, 10752, 11264, 23552, 24576, 51200, 53248, 110592, 114688, 237568, 245760, 507904, 524288, 1081344, 1114112, 2293760, 2359296, 4849664, 4980736, 10223616, 10485760, 21495808, 22020096, 45088768, 46137344
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: (x + 3*x^2 - 2*x^4)/(1 - 2*x^2)^2.
a(n) = Sum_{k=1..n} A051159(n,k)*k.
a(2k) = (2k+1)*2^(k-1) for k>0, a(2k+1) = (2k+2)*2^(k-1) for k>=0. - Gregory L. Simay, Dec 05 2022
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EXAMPLE
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a(5)=12 because we have: 5, 1+3+1, 2+1+2, 1+1+1+1+1 with a total of 12 parts.
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MATHEMATICA
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nn=30; r=Solve[p==y/(1-x) - y + 1 + y^2*x^2/(1-x^2)*p, p]; CoefficientList[Series[D[p/.r, y]/.y->1, {x, 0, nn}], x]
CoefficientList[Series[(x + 3 x^2 - 2 x^4)/(1 - 2 x^2)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 23 2014 *)
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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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