A268514 a(0)=0; thereafter a(2n+1)=3*a(n)+1, a(2n)=2*a(n)+a(n-1)+1.

0, 1, 3, 4, 8, 10, 12, 13, 21, 25, 29, 31, 35, 37, 39, 40, 56, 64, 72, 76, 84, 88, 92, 94, 102, 106, 110, 112, 116, 118, 120, 121, 153, 169, 185, 193, 209, 217, 225, 229, 245, 253, 261, 265, 273, 277, 281, 283, 299, 307, 315, 319, 327, 331, 335, 337

Offset: 0

Author

N. J. A. Sloane, Feb 07 2016

Keywords

• nonn

Links

• Colin Barker, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A064194, A023416 (no. of 0's in n).

First differences are (essentially) A080100.

Programs

PARI

a(n) = sum(i=1, n, b=binary(i); 2^(#b-norml2(b))) \\ Colin Barker, Feb 08 2016

Formula

a(n) = Sum{i=1..n} 2^{number of 0's in binary expansion of i}.

a(n) = (A064194(n+1)-1)/2.