A350094 a(n) = Sum_{k=0..n} n CNIMPL k where CNIMPL = NOT(n) AND k is the bitwise logical converse non-implication operator (A102037).

0, 0, 1, 0, 6, 4, 3, 0, 28, 24, 21, 16, 18, 12, 7, 0, 120, 112, 105, 96, 94, 84, 75, 64, 84, 72, 61, 48, 42, 28, 15, 0, 496, 480, 465, 448, 438, 420, 403, 384, 396, 376, 357, 336, 322, 300, 279, 256, 360, 336, 313, 288, 270, 244, 219, 192, 196, 168, 141, 112

Offset: 0

Author

Kevin Ryde, Dec 14 2021

Keywords

• base
• easy
• nonn

Comments

The effect of NOT(n) AND k is to retain from k only those bits where n has a 0-bit. Conversely n AND k retains from k those bits where n has a 1-bit. Together they are all bits of k so that a(n) + A222423(n) = Sum_{k=0..n} k = n*(n+1)/2.

Crossrefs

Row sums of A102037.

Cf. A001196 (bit doubling).

Other sums: A222423 (AND), A350093 (OR), A224915 (XOR), A265736 (IMPL).

Programs

Maple

with(Bits): cnimp := (n, k) -> And(Not(n), k):
seq(add(cnimp(n, k), k = 0..n), n = 0..59); # Peter Luschny, Dec 14 2021

PARI

a(n) = (3*fromdigits(binary(n),4) - n^2 - 2*n)/4;

Formula

a(n) = (A001196(n) - n*(n+2))/4.

a(2*n) = 4*a(n) + n.

a(2*n+1) = 4*a(n).