A099027 a(n) = Sum_{k=0..n} n-k AND NOT k.

0, 1, 2, 6, 6, 11, 16, 28, 24, 29, 34, 50, 54, 71, 88, 120, 104, 105, 106, 126, 126, 147, 168, 212, 208, 229, 250, 298, 318, 367, 416, 496, 448, 433, 418, 438, 422, 443, 464, 524, 504, 525, 546, 610, 630, 695, 760, 872, 840, 857, 874, 942, 958, 1027, 1096

Offset

0,3

Comments

Antidiagonal sums of array A099026.

Links

Michel Marcus, Table of n, a(n) for n = 0..8191

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, p. 39.

Formula

Recurrence: a(0) = 0, a(2n) = 2a(n) + 2a(n+1), a(2n+1) = 4a(n) + n+1.

Prog

(PARI) a(n) = sum(k=0, n, bitand(n-k, bitneg(k))); \\ Michel Marcus, Oct 30 2022

Crossrefs

Cf. A006581, A006582, A006583.

Sequence in context: A200579 A200809 A323444 * A306925 A134466 A062562

Adjacent sequences: A099024 A099025 A099026 * A099028 A099029 A099030

Keyword

nonn

Author

Ralf Stephan, Sep 26 2004

Status

approved