A328566 a(n) is the sum of the elements of the set O_n = {(n-k) OR k, k = 0..n} (where OR denotes the bitwise OR operator).

0, 0, 1, 3, 3, 9, 8, 14, 7, 25, 21, 37, 18, 46, 31, 45, 15, 65, 54, 96, 45, 119, 79, 115, 38, 130, 97, 159, 65, 155, 94, 124, 31, 161, 135, 243, 112, 304, 199, 289, 93, 331, 246, 404, 163, 393, 237, 313, 78, 338, 267, 461, 199, 517, 326, 456, 133, 443, 317, 505

Offset

-1,4

Comments

The number of elements of the set O_n appears to be A002487(n+1); a(-1) = 0 as O_{-1} is the empty set.

Row sums of A326820.

Links

Rémy Sigrist, Table of n, a(n) for n = -1..8192

Rémy Sigrist, Scatterplot of (x, y) where x = 0..1023 and y belongs to O_x

Formula

a(n) <= n + A006583(n) for n >= 2.

Maple

a:= n-> add(i, i={seq(Bits[Or](n-k, k), k=0..n)}):
seq(a(n), n=-1..80);  # Alois P. Heinz, Oct 20 2019

Prog

(PARI) a(n) = vecsum(Set(apply(k -> bitor(k, n-k), [0..n])))
(Python)
def A328566(n): return sum(set(k|n-k for k in range((n>>1)+1))) # Chai Wah Wu, May 07 2023

Crossrefs

Cf. A328564 (AND variant), A328565 (XOR variant).

Cf. A002487, A006583, A326820.

Sequence in context: A019745 A173815 A188615 * A362046 A155686 A290300

Adjacent sequences: A328563 A328564 A328565 * A328567 A328568 A328569

Keyword

nonn,base

Author

Rémy Sigrist, Oct 20 2019

Status

approved