A094120 a(n) = Sum_{k=1..n} Sum_{i=1..k} (-2)^valuation(i,2).

0, 1, 0, 0, 4, 9, 12, 16, 12, 9, 4, 0, 0, 1, 0, 0, 16, 33, 48, 64, 84, 105, 124, 144, 156, 169, 180, 192, 208, 225, 240, 256, 240, 225, 208, 192, 180, 169, 156, 144, 124, 105, 84, 64, 48, 33, 16, 0, 0, 1, 0, 0, 4, 9, 12, 16, 12, 9, 4, 0, 0, 1, 0, 0, 64, 129, 192, 256, 324, 393

Offset

0,5

Links

Michael De Vlieger, Table of n, a(n) for n = 0..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, pp. 49-51.

Mathematica

{0}~Join~Accumulate@ Accumulate@ Array[(-2)^IntegerExponent[#, 2] &, 69] (* Michael De Vlieger, Oct 30 2022 *)

Prog

(PARI) a(n)=sum(k=1, n, sum(i=1, k, (-2)^valuation(i, 2)))

Crossrefs

Cf. A006519.

Sequence in context: A312853 A312854 A010386 * A066423 A355571 A072498

Adjacent sequences: A094117 A094118 A094119 * A094121 A094122 A094123

Keyword

nonn

Author

Benoit Cloitre, May 03 2004

Status

approved