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%I #16 May 08 2023 02:10:46
%S 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,
%T 92,69,110,49,114,72,98,31,130,105,180,84,212,139,198,69,222,164,262,
%U 111,258,159,212,62,244,191,322,143,358,228,318,101,326,235,372,148
%N 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).
%C 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.
%C Row sums of A328568.
%H Rémy Sigrist, <a href="/A328565/b328565.txt">Table of n, a(n) for n = -1..8192</a>
%H Rémy Sigrist, <a href="/A328565/a328565.png">Scatterplot of (x, y) where x = 0..1023 and y belongs to X_x</a>
%F a(n) <= n + A006582(n) for n >= 2.
%p a:= n-> add(i, i={seq(Bits[Xor](n-k, k), k=0..n)}):
%p seq(a(n), n=-1..80); # _Alois P. Heinz_, Oct 20 2019
%o (PARI) a(n) = vecsum(Set(apply(k -> bitxor(k, n-k), [0..n])))
%o (Python)
%o def A328565(n): return sum(set(k^n-k for k in range((n>>1)+1))) # _Chai Wah Wu_, May 07 2023
%Y Cf. A328564 (AND variant), A328566 (OR variant).
%Y Cf. A002487, A006582, A328568.
%K nonn,base
%O -1,4
%A _Rémy Sigrist_, Oct 20 2019
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