%I #9 Feb 24 2021 02:48:18

%S 1,2,4,8,4,8,16,20,4,8,16,20,16,32,52,44,4,8,16,20,16,32,52,44,16,32,

%T 52,56,64,116,148,92,4,8,16,20,16,32,52,44,16,32,52,56,64,116,148,92,

%U 16,32,52,56,64,116,148,104,64,116,160,176,244,380,388,188,4,8,16,20,16,32,52

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

%C Equals 2*A160552+A151704.

%H Ivan Neretin, <a href="/A151569/b151569.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>

%t a = {1, 2}; 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.

%Y Cf. A139250, A160552, A151568.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, May 25 2009