A328565 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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