%I #9 Feb 24 2021 02:48:19

%S 1,0,2,6,2,6,22,18,2,6,22,18,22,78,98,42,2,6,22,18,22,78,98,42,22,78,

%T 98,102,278,450,322,90,2,6,22,18,22,78,98,42,22,78,98,102,278,450,322,

%U 90,22,78,98,102,278,450,322,150,278,450,502,1038,1906,1866,914,186,2,6,22,18

%N a(0) = 1, a(1) = 0; a(2^i + j) = 2a(j) + 3a(j + 1) for 0 <= j < 2^i.

%H Robert Israel, <a href="/A170861/b170861.txt">Table of n, a(n) for n = 0..10000</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 A[0]:= 1:A[1]:= 0:

%p for d from 1 to 7 do

%p for j from 0 to 2^d-1 do

%p A[2^d+j]:= 2*A[j]+3*A[j+1]

%p od od:

%p seq(A[i],i=0..2^8-1); # _Robert Israel_, Mar 22 2017

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jan 02 2010