A087733 Partial sums of A068639.

0, 1, 1, 2, 4, 7, 9, 12, 14, 17, 19, 22, 26, 31, 35, 40, 46, 53, 59, 66, 74, 83, 91, 100, 108, 117, 125, 134, 144, 155, 165, 176, 186, 197, 207, 218, 230, 243, 255, 268, 280, 293, 305, 318, 332, 347, 361, 376, 392, 409, 425, 442, 460, 479, 497, 516, 534, 553, 571

Offset

0,4

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

J.-P. Allouche and Jeffrey Shallit, The Ring of k-regular Sequences, II

J.-P. Allouche and Jeffrey Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.

Hsien-Kuei Hwang, S. Janson, and T.-H. Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016.

Hsien-Kuei Hwang, S. Janson, and T.-H. Tsai, Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47.

Formula

a(0)=0, a(2n+1) = -a(n)-a(n+1)+n^2+n, a(2n+1) = -2a(n)+n^2+2n+1. - Ralf Stephan, Oct 16 2003

Mathematica

Join[{0}, Nest[Accumulate, (-1)^IntegerExponent[Range[100], 2], 2]] (* Paolo Xausa, Jun 04 2025 *)

Crossrefs

Sequence in context: A047211 A225000 A189677 * A065027 A165994 A163293

Adjacent sequences: A087730 A087731 A087732 * A087734 A087735 A087736

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 01 2003

Extensions

More terms from Benoit Cloitre, Oct 04 2003

Status

approved