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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). 4
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

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])))

CROSSREFS

Cf. A328564 (AND variant), A328566 (OR variant).

Cf. A002487, A006582, A328568.

Sequence in context: A039799 A185423 A144583 * A308762 A155215 A119319

Adjacent sequences:  A328562 A328563 A328564 * A328566 A328567 A328568

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Oct 20 2019

STATUS

approved

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Last modified August 9 03:22 EDT 2022. Contains 356016 sequences. (Running on oeis4.)