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A048641
Partial sums of A003188 (Gray code).
3
0, 1, 4, 6, 12, 19, 24, 28, 40, 53, 68, 82, 92, 103, 112, 120, 144, 169, 196, 222, 252, 283, 312, 340, 360, 381, 404, 426, 444, 463, 480, 496, 544, 593, 644, 694, 748, 803, 856, 908, 968, 1029, 1092, 1154, 1212, 1271, 1328, 1384, 1424, 1465, 1508, 1550, 1596
OFFSET
1,3
LINKS
Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, pp. 39-40.
FORMULA
a(2^n-1) = A000217(2^n-1) for all n.
a(n) = Sum_{j=0..n} XORnos(j, floor(j/2)).
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
MATHEMATICA
Accumulate[Table[BitXor[n, Floor[n/2]], {n, 0, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *)
PROG
(PARI) a(n) = sum(k=0, n, bitxor(k, k>>1)); \\ Michel Marcus, Oct 02 2015
CROSSREFS
Sequence in context: A079865 A059961 A027856 * A023599 A087881 A063607
KEYWORD
easy,nonn
AUTHOR
Antti Karttunen, Jul 14 1999
STATUS
approved