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A029886
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Convolution of Thue-Morse sequence A001285 with itself.
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10
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1, 4, 8, 10, 12, 14, 15, 16, 22, 24, 23, 26, 29, 30, 34, 40, 38, 40, 43, 42, 47, 50, 52, 56, 55, 56, 62, 66, 64, 70, 71, 64, 78, 80, 75, 82, 83, 82, 88, 96, 89, 92, 100, 98, 102, 106, 105, 104, 111, 112, 114, 122, 118, 122, 125, 120, 130, 136, 131, 130, 141, 134, 138, 160
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1/4)*(3/(1 - x) - Product_{k>=0} (1 - x^(2^k)))^2. - Ilya Gutkovskiy, Apr 03 2019
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MATHEMATICA
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P[n_, x_] := (bb = IntegerDigits[n, 2]) . x^Range[Length[bb]-1, 0, -1];
TM[n_] := 1 + Mod[P[n, 1], 2];
a[n_] := Sum[TM[k] TM[n-k], {k, 0, n}];
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PROG
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(PARI) a(n)=sum(k=0, n, (1+subst(Pol(binary(k)), x, 1)%2)*(1+subst(Pol(binary(n-k)), x, 1)%2)) \\ Ralf Stephan, Aug 23 2013
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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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