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
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.
Programs
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Mathematica
Join[{0}, Nest[Accumulate, (-1)^IntegerExponent[Range[100], 2], 2]] (* Paolo Xausa, Jun 04 2025 *)
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
Extensions
More terms from Benoit Cloitre, Oct 04 2003