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 A151571 #11 Feb 24 2021 02:48:18
%S A151571 1,2,3,5,3,5,8,8,3,5,8,8,8,13,16,11,3,5,8,8,8,13,16,11,8,13,16,16,21,
%T A151571 29,27,14,3,5,8,8,8,13,16,11,8,13,16,16,21,29,27,14,8,13,16,16,21,29,
%U A151571 27,19,21,29,32,37,50,56,41,17,3,5,8,8,8,13,16,11,8,13,16,16,21,29,27,14,8,13
%N A151571 a(0)=1, a(1)=2; a(2^i + j) = a(j) + a(j+1) for 0 <= j < 2^i.
%C A151571 Equals 2*A118977 + A151702.
%H A151571 Ivan Neretin, <a href="/A151571/b151571.txt">Table of n, a(n) for n = 0..8191</a>
%H A151571 David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
%H A151571 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>
%t A151571 a = {1, 2}; Do[AppendTo[a, a[[j]] + a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* _Ivan Neretin_, Jun 28 2017 *)
%Y A151571 For the recurrence a(2^i+j) = C*a(j) + D*a(j+1), a(0) = A, a(1) = B for following values of (A B C D) see: (0 1 1 1) A118977, (1 0 1 1) A151702, (1 1 1 1) A151570, (1 2 1 1) A151571, (0 1 1 2) A151572, (1 0 1 2) A151703, (1 1 1 2) A151573, (1 2 1 2) A151574, (0 1 2 1) A160552, (1 0 2 1) A151704, (1 1 2 1) A151568, (1 2 2 1) A151569, (0 1 2 2) A151705, (1 0 2 2) A151706, (1 1 2 2) A151707, (1 2 2 2) A151708.
%K A151571 nonn
%O A151571 0,2
%A A151571 _N. J. A. Sloane_, May 25 2009