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%I A048644 #11 Oct 29 2022 11:50:26
%S A048644 0,0,1,0,2,4,3,0,4,8,13,16,14,12,7,0,8,16,25,32,42,52,59,64,60,56,53,
%T A048644 48,38,28,15,0,16,32,49,64,82,100,115,128,148,168,189,208,222,236,247,
%U A048644 256,248,240,233,224,218,212,203,192,172,152,133,112,86,60,31,0,32,64
%N A048644 Differences between partial sums of Gray code (A048641) and triangular numbers (A000217).
%C A048644 a(2^n-1) = 0 for all n.
%H A048644 Michael De Vlieger, <a href="/A048644/b048644.txt">Table of n, a(n) for n = 0..10000</a>
%H A048644 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, p. 40.
%F A048644 a(n) = sum(XORnos(j, floor(j/2)), j=0..n)-((n^2+n)/2).
%t A048644 {0}~Join~MapIndexed[#1 - PolygonalNumber[First[#2]] &, Accumulate[Array[BitXor[#, Floor[#/2]] &, 65]]] (* _Michael De Vlieger_, Oct 29 2022 *)
%o A048644 (PARI) a(n) = sum(k=0, n, bitxor(k, k>>1)) - n*(n+1)/2; \\ _Michel Marcus_, Oct 02 2015
%Y A048644 Cf. A000217, A048461, A048643.
%K A048644 easy,nonn
%O A048644 0,5
%A A048644 _Antti Karttunen_, Jul 14 1999
%E A048644 Corrected by _Don Reble_, May 01 2006

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