A171378 a(n) = (n+1)^2 - A006046(n+1).

0, 1, 4, 7, 14, 21, 30, 37, 52, 67, 84, 99, 120, 139, 160, 175, 206, 237, 270, 301, 338, 373, 410, 441, 486, 529, 574, 613, 662, 705, 750, 781, 844, 907, 972, 1035, 1104, 1171, 1240, 1303, 1380, 1455, 1532, 1603, 1684, 1759, 1836, 1899, 1992, 2083, 2176, 2263

Offset

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000 (a(0..999) from Robert Price)

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. 6, 30.

Mathematica

Table[(n+1)^2 -Sum[Sum[Mod[Binomial[m, k], 2], {k, 0, m}], {m, 0, n}], {n, 0, 60}]
a[0] = 0; a[1] = 1; a[n_] := a[n] = 2 a[Floor[#]] + a[Ceiling[#]] &[n/2]; Array[(# + 1)^2 - a[# + 1] &, 52, 0] (* Michael De Vlieger, Nov 01 2022 *)

Prog

(PARI) {a(n) = (n+1)^2 - sum(m=0, n, sum(k=0, m, binomial(m, k)%2))};
for(n=0, 60, print1(a(n), ", ")) \\ G. C. Greubel, Apr 11 2019
(Magma) [(n+1)^2 - (&+[ (&+[ Binomial(m, k) mod 2: k in [0..m]]): m in [0..n]]): n in [0..60]]; // G. C. Greubel, Apr 11 2019
(Sage) [(n+1)^2 - sum(sum(binomial(m, k)%2 for k in (0..m)) for m in (0..n)) for n in (0..60)] # G. C. Greubel, Apr 11 2019

Crossrefs

Cf. A006046, A001316.

Sequence in context: A157615 A338551 A188319 * A147478 A147372 A201272

Adjacent sequences: A171375 A171376 A171377 * A171379 A171380 A171381

Keyword

nonn,easy

Author

Roger L. Bagula, Dec 07 2009

Extensions

Edited by G. C. Greubel, Apr 11 2019

Definition corrected by Georg Fischer, Jun 21 2020

Status

approved