A151788 Partial sums of A151787.

1, 4, 7, 13, 16, 22, 28, 40, 43, 49, 55, 67, 73, 85, 97, 121, 124, 130, 136, 148, 154, 166, 178, 202, 208, 220, 232, 256, 268, 292, 316, 364, 367, 373, 379, 391, 397, 409, 421, 445, 451, 463, 475, 499, 511, 535, 559, 607, 613, 625, 637, 661, 673, 697, 721, 769, 781, 805

Offset: 1

Author

N. J. A. Sloane, Jun 25 2009

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 30.

Crossrefs

Cf. A151787.

Programs

Maple

wt:= n -> convert(convert(n,base,2),`+`):
ListTools:-PartialSums([1,seq(3*2^(wt(n-1)-1),n=2..100)]); # Robert Israel, Feb 27 2018

Mathematica

b[n_] := If[n == 1, 1, 3*2^(Total[IntegerDigits[n-1, 2]]-1)];
Array[b, 100] // Accumulate (* Jean-François Alcover, Mar 27 2019 *)

PARI

b(n) = if (n==1, 1, 3*2^(hammingweight(n-1)-1));
a(n) = sum(k=1, n, b(k)); \\ Michel Marcus, Feb 27 2018

Formula

G.f. g(x) satisfies g(x) = (2+1/x)*(1+x)*g(x^2) + x^2/(1-x). - Robert Israel, Feb 27 2018