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

0,5

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.

Links

Table of n, a(n) for n=0..59.

Formula

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

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

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

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

Prog

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

Crossrefs

Row sums of A102037.

Cf. A001196 (bit doubling).

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

Sequence in context: A158233 A093604 A011408 * A197760 A217290 A157296

Adjacent sequences: A350091 A350092 A350093 * A350095 A350096 A350097

Keyword

base,easy,nonn

Author

Kevin Ryde, Dec 14 2021

Status

approved