This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A099027 #29 Sep 30 2024 06:10:35
%S A099027 0,1,2,6,6,11,16,28,24,29,34,50,54,71,88,120,104,105,106,126,126,147,
%T A099027 168,212,208,229,250,298,318,367,416,496,448,433,418,438,422,443,464,
%U A099027 524,504,525,546,610,630,695,760,872,840,857,874,942,958,1027,1096
%N A099027 a(n) = Sum_{k=0..n} n-k AND NOT k.
%C A099027 Antidiagonal sums of array A099026.
%H A099027 Michel Marcus, <a href="/A099027/b099027.txt">Table of n, a(n) for n = 0..8191</a>
%H A099027 Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2210.10968">Identities and periodic oscillations of divide-and-conquer recurrences splitting at half</a>, arXiv:2210.10968 [cs.DS], 2022, p. 39.
%F A099027 Recurrence: a(0) = 0, a(2n) = 2a(n) + 2a(n-1), a(2n+1) = 4a(n) + n+1. [corrected by _Peter J. Taylor_, May 30 2024]
%t A099027 (* Using definition *)
%t A099027 Table[Sum[BitAnd[n - k, BitNot[k]], {k, 0, n}], {n, 0, 100}]
%t A099027 (* Using recurrence -- faster *)
%t A099027 a[0] = 0; a[n_] := a[n] = If[OddQ[n], 4*a[(n-1)/2] + (n-1)/2 + 1, 2*(a[n/2] + a[n/2-1])];
%t A099027 Table[a[n], {n, 0, 100}] (* _Paolo Xausa_, Sep 30 2024 *)
%o A099027 (PARI) a(n) = sum(k=0, n, bitand(n-k, bitneg(k))); \\ _Michel Marcus_, Oct 30 2022
%Y A099027 Cf. A006581, A006582, A006583, A099026.
%K A099027 nonn
%O A099027 0,3
%A A099027 _Ralf Stephan_, Sep 26 2004