A170858 - OEIS

A170858

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

%I #6 Feb 24 2021 02:48:19

%S 1,0,3,3,3,3,12,12,3,3,12,12,12,21,48,39,3,3,12,12,12,21,48,39,12,21,

%T 48,48,57,111,183,120,3,3,12,12,12,21,48,39,12,21,48,48,57,111,183,

%U 120,12,21,48,48,57,111,183,129,57,111,192,201,282,516,669,363,3,3,12,12,12,21

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

%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>

%K nonn

%O 0,3

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