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%I #13 Oct 30 2022 11:05:35
%S 0,1,0,0,4,9,12,16,12,9,4,0,0,1,0,0,16,33,48,64,84,105,124,144,156,
%T 169,180,192,208,225,240,256,240,225,208,192,180,169,156,144,124,105,
%U 84,64,48,33,16,0,0,1,0,0,4,9,12,16,12,9,4,0,0,1,0,0,64,129,192,256,324,393
%N a(n) = Sum_{k=1..n} Sum_{i=1..k} (-2)^valuation(i,2).
%H Michael De Vlieger, <a href="/A094120/b094120.txt">Table of n, a(n) for n = 0..10000</a>
%H Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2210.10968">Identities and periodic oscillations of divide-and-conquer recurrences splitting at half</a>, arXiv:2210.10968 [cs.DS], 2022, pp. 49-51.
%t {0}~Join~Accumulate@ Accumulate@ Array[(-2)^IntegerExponent[#, 2] &, 69] (* _Michael De Vlieger_, Oct 30 2022 *)
%o (PARI) a(n)=sum(k=1,n,sum(i=1,k,(-2)^valuation(i,2)))
%Y Cf. A006519.
%K nonn
%O 0,5
%A _Benoit Cloitre_, May 03 2004
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