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

1,3

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

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

Cf. A000217, A003188.

Sequence in context: A079865 A059961 A027856 * A023599 A087881 A063607

Adjacent sequences: A048638 A048639 A048640 * A048642 A048643 A048644

Keyword

easy,nonn

Author

Antti Karttunen, Jul 14 1999

Status

approved