A048641 Partial sums of A003188 (Gray code).
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
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10001
- 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.
- R. Stephan, Some divide-and-conquer sequences ...
- R. Stephan, Table of generating functions
Programs
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Mathematica
Accumulate[Table[BitXor[n, Floor[n/2]], {n, 0, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *) -
PARI
a(n) = sum(k=0, n, bitxor(k, k>>1)); \\ Michel Marcus, Oct 02 2015
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