A328564 a(n) is the sum of the elements of the set A_n = {(n-k) AND k, k = 0..n} (where AND denotes the bitwise AND operator).

0, 0, 0, 1, 0, 3, 2, 4, 0, 7, 6, 13, 4, 14, 8, 11, 0, 15, 14, 30, 12, 41, 26, 39, 8, 38, 28, 49, 16, 41, 22, 26, 0, 31, 30, 63, 28, 92, 60, 91, 24, 109, 82, 142, 52, 135, 78, 101, 16, 94, 76, 139, 56, 159, 98, 138, 32, 117, 82, 133, 44, 100, 52, 57, 0, 63, 62

Offset

-1,6

Comments

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

Row sums of A326819.

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 A_x

Formula

a(n) <= A006581(n).

Apparently, a(n) + A328565(n) = A328566(n).

Maple

a:= n-> add(i, i={seq(Bits[And](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 -> bitand(k, n-k), [0..n])))
(Python)
def A328564(n): return sum(set(k&n-k for k in range((n>>1)+1))) # Chai Wah Wu, May 07 2023

Crossrefs

Cf. A328565 (XOR variant), A328566 (OR variant).

Cf. A002487, A006581, A326819.

Sequence in context: A004545 A127481 A284552 * A154879 A097673 A226377

Adjacent sequences: A328561 A328562 A328563 * A328565 A328566 A328567

Keyword

nonn,look,base

Author

Rémy Sigrist, Oct 20 2019

Status

approved