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%I #22 Oct 29 2022 11:50:29
%S 0,1,4,6,12,19,24,28,40,53,68,82,92,103,112,120,144,169,196,222,252,
%T 283,312,340,360,381,404,426,444,463,480,496,544,593,644,694,748,803,
%U 856,908,968,1029,1092,1154,1212,1271,1328,1384,1424,1465,1508,1550,1596
%N Partial sums of A003188 (Gray code).
%H Michael De Vlieger, <a href="/A048641/b048641.txt">Table of n, a(n) for n = 1..10001</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. 39-40.
%H R. Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>
%H R. Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>
%F a(2^n-1) = A000217(2^n-1) for all n.
%F a(n) = Sum_{j=0..n} XORnos(j, floor(j/2)).
%F a(n) = b(n-1), with b(2n) = 2*(b(n) + b(n-1) + ceiling(n/2)), b(2n+1) = 4*b(n) + n + 1. - _Ralf Stephan_, Sep 13 2003
%t Accumulate[Table[BitXor[n, Floor[n/2]], {n, 0, 100}]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 19 2011 *)
%o (PARI) a(n) = sum(k=0, n, bitxor(k, k>>1)); \\ _Michel Marcus_, Oct 02 2015
%Y Cf. A000217, A003188.
%K easy,nonn
%O 1,3
%A _Antti Karttunen_, Jul 14 1999
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