%I #11 Feb 24 2021 02:48:18
%S 1,0,2,2,2,2,6,6,2,2,6,6,6,10,18,14,2,2,6,6,6,10,18,14,6,10,18,18,22,
%T 38,50,30,2,2,6,6,6,10,18,14,6,10,18,18,22,38,50,30,6,10,18,18,22,38,
%U 50,34,22,38,54,58,82,126,130,62,2,2,6,6,6,10,18,14,6,10,18,18,22,38,50,30,6
%N a(0)=1, a(1)=0; a(2^i+j) = 2*a(j) + a(j+1) for 0 <= j < 2^i.
%H Ivan Neretin, <a href="/A151704/b151704.txt">Table of n, a(n) for n = 0..8191</a>
%H 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 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>
%p See A151702 for Maple code.
%t a = {1, 0}; Do[AppendTo[a, 2 a[[j]] + a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* _Ivan Neretin_, Jul 04 2017 *)
%Y 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 nonn
%O 0,3
%A _N. J. A. Sloane_, Jun 06 2009