A350093 a(n) = Sum_{k=0..n} n OR k where OR is the bitwise logical OR operator (A003986).

0, 2, 7, 12, 26, 34, 45, 56, 100, 114, 131, 148, 174, 194, 217, 240, 392, 418, 447, 476, 514, 546, 581, 616, 684, 722, 763, 804, 854, 898, 945, 992, 1552, 1602, 1655, 1708, 1770, 1826, 1885, 1944, 2036, 2098, 2163, 2228, 2302, 2370, 2441, 2512, 2712, 2786, 2863

Offset

0,2

Comments

The effect of n OR k is to force a 1-bit at all bit positions where n has a 1-bit, which means n*(n+1) in the sum. Bits of k where n has a 0-bit are NOT(n) AND k = n CNIMPL k so that a(n) = A350094(n) + n*(n+1).

Links

Winston de Greef, Table of n, a(n) for n = 0..10000

Formula

a(n) = ((3*n+2)*n + A001196(n)) / 4.

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

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

a(n) = A222423(n) + A224915(n), being OR = AND + XOR.

Prog

(PARI) a(n) = (3*(n^2 + fromdigits(binary(n), 4)) + 2*n) >> 2;

Crossrefs

Cf. A003986 (bitwise OR), A001196 (bit doubling).

Row sums of A080098.

Other sums: A222423 (AND), A224915 (XOR), A265736 (IMPL), A350094 (CNIMPL).

Sequence in context: A079824 A059329 A242201 * A177747 A288888 A293621

Adjacent sequences: A350090 A350091 A350092 * A350094 A350095 A350096

Keyword

base,easy,nonn

Author

Kevin Ryde, Dec 14 2021

Status

approved