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 A266535 #34 Feb 26 2023 19:42:26
%S A266535 0,1,3,7,11,15,23,35,43,47,55,67,83,103,127,155,171,175,183,195,211,
%T A266535 231,255,283,315,351,391,435,483,535,591,651,683,687,695,707,723,743,
%U A266535 767,795,827,863,903,947,995,1047,1103,1163,1227,1295,1367,1443,1523,1607,1695,1787,1883,1983,2087,2195,2307,2423,2543,2667,2731
%N A266535 Sums of two successive terms of A256249, with a(0) = 0.
%C A266535 Also bisection of A266540.
%C A266535 It appears that this sequence has a fractal-like behavior (see Plot 2, A139250 vs. this sequence).
%C A266535 First differs from both the toothpick sequence A139250 and A256265 at a(12), with which it shares infinitely many terms.
%H A266535 Michel Marcus, <a href="/A266535/b266535.txt">Table of n, a(n) for n = 0..10000</a>
%H A266535 N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%H A266535 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%t A266535 Most@ # + Rest@ # &@ Accumulate@ Join[{0, 0}, Flatten@ Table[Range[1, 2^n - 1, 2], {n, 0, 6}]] (* _Michael De Vlieger_, Jan 05 2016, after _Ivan N. Ianakiev_ at A256249 *)
%o A266535 (PARI) f(n)=n++; b=#binary(n>>1); (4^b-1)/3+(n-2^b)^2; \\ A256249
%o A266535 a(n) = if (n, f(n)+f(n-1), 0);
%Y A266535 Cf. A006257, A139250, A256249, A256265, A266539, A266540.
%K A266535 nonn
%O A266535 0,3
%A A266535 _Omar E. Pol_, Jan 02 2016