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

1,2

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.

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

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 *)

Prog

(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

Crossrefs

Cf. A151787.

Sequence in context: A310806 A125758 A259566 * A310807 A310808 A310809

Adjacent sequences: A151785 A151786 A151787 * A151789 A151790 A151791

Keyword

nonn

Author

N. J. A. Sloane, Jun 25 2009

Status

approved