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A151568 a(0)=1, a(1)=1; a(2^i+j)=2*a(j)+a(j+1) for 0 <= j < 2^i.

%I A151568 #9 Feb 24 2021 02:48:18
%S A151568 1,1,3,5,3,5,11,13,3,5,11,13,11,21,35,29,3,5,11,13,11,21,35,29,11,21,
%T A151568 35,37,43,77,99,61,3,5,11,13,11,21,35,29,11,21,35,37,43,77,99,61,11,
%U A151568 21,35,37,43,77,99,69,43,77,107,117,163,253,259,125,3,5,11,13,11,21,35,29,11
%N A151568 a(0)=1, a(1)=1; a(2^i+j)=2*a(j)+a(j+1) for 0 <= j < 2^i.
%C A151568 Equals A160552+A151704.
%H A151568 Ivan Neretin, <a href="/A151568/b151568.txt">Table of n, a(n) for n = 0..8191</a>
%H A151568 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 A151568 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 A151568 a = {1, 1}; Do[AppendTo[a, 2 a[[j]] + a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* _Ivan Neretin_, Jul 04 2017 *)
%Y A151568 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.
%Y A151568 Cf. A139250, A160552, A151569.
%K A151568 nonn
%O A151568 0,3
%A A151568 _N. J. A. Sloane_, May 25 2009