A328565 a(n) is the sum of the elements of the set X_n = {(n-k) XOR k, k = 0..n} (where XOR denotes the bitwise XOR operator).

0, 0, 1, 2, 3, 6, 6, 10, 7, 18, 15, 24, 14, 32, 23, 34, 15, 50, 40, 66, 33, 78, 53, 76, 30, 92, 69, 110, 49, 114, 72, 98, 31, 130, 105, 180, 84, 212, 139, 198, 69, 222, 164, 262, 111, 258, 159, 212, 62, 244, 191, 322, 143, 358, 228, 318, 101, 326, 235, 372, 148

Offset

-1,4

Comments

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

Row sums of A328568.

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 X_x

Formula

a(n) <= n + A006582(n) for n >= 2.

Maple

a:= n-> add(i, i={seq(Bits[Xor](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 -> bitxor(k, n-k), [0..n])))
(Python)
def A328565(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), A328566 (OR variant).

Cf. A002487, A006582, A328568.

Sequence in context: A039799 A185423 A144583 * A308762 A155215 A363075

Adjacent sequences: A328562 A328563 A328564 * A328566 A328567 A328568

Keyword

nonn,base

Author

Rémy Sigrist, Oct 20 2019

Status

approved