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 A151572 #11 Feb 24 2021 02:48:18
%S A151572 0,1,2,5,2,5,12,9,2,5,12,9,12,29,30,13,2,5,12,9,12,29,30,13,12,29,30,
%T A151572 33,70,89,56,17,2,5,12,9,12,29,30,13,12,29,30,33,70,89,56,17,12,29,30,
%U A151572 33,70,89,56,37,70,89,96,173,248,201,90,21,2,5,12,9,12,29,30,13,12,29,30,33,70
%N A151572 a(0)=0, a(1)=1; a(2^i + j) = a(j) + 2*a(j+1) for 0 <= j < 2^i.
%H A151572 Ivan Neretin, <a href="/A151572/b151572.txt">Table of n, a(n) for n = 0..8191</a>
%H A151572 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 A151572 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 A151572 a = {0, 1}; Do[AppendTo[a, a[[j]] + 2 a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* _Ivan Neretin_, Jun 28 2017 *)
%Y A151572 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 A151572 nonn
%O A151572 0,3
%A A151572 _N. J. A. Sloane_, May 25 2009