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%I #8 Sep 04 2019 23:59:26
%S 0,1,1,0,2,-1,1,2,2,-3,1,2,0,1,3,0,4,-5,-1,4,-2,1,3,-2,2,1,1,2,4,-3,3,
%T 4,4,-9,-1,4,-6,5,3,-6,2,3,-1,2,4,-5,1,4,0,-1,3,0,2,1,3,2,6,-7,1,6,0,
%U 1,7,0,8,-13,-5,8,-10,5,3,-10,-2,11,-1,-2
%N a(0) = 0, a(1) = 1; a(2*n) = a(n-1) + a(n), a(2*n+1) = a(n+1) - a(n).
%H Ilya Gutkovskiy, <a href="/A325055/a325055.jpg">Scatter plot of a(n) up to n=50000</a>
%F a(n) = Sum_{k=1..n} a(2*k-1) = Sum_{k=1..n} (-1)^(n-k) * a(2*k).
%F a(2^k) = 2^floor(k/2).
%t a[0] = 0; a[1] = 1; a[n_] := a[n] = If[EvenQ[n], a[(n - 2)/2] + a[n/2], a[(n + 1)/2] - a[(n - 1)/2]]; Table[a[n], {n, 0, 75}]
%Y Cf. A001196 (positions of 0's), A002487, A005590, A075825.
%K sign
%O 0,5
%A _Ilya Gutkovskiy_, Sep 04 2019
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