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a(n) = A173531(n) - A139251(n).
2

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

%S 0,0,0,0,0,0,0,4,0,0,0,4,4,0,4,32,0,0,0,4,4,0,4,32,12,0,4,28,24,4,40,

%T 176,0,0,0,4,4,0,4,32,12,0,4,28,24,4,40,176,28,0,4,28,24,4,40,172,72,

%U 4,36,144,116,48,256,832,0,0,0,4,4,0,4,32,12,0,4

%N a(n) = A173531(n) - A139251(n).

%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>

%e If written as a triangle, begins:

%e 0;

%e 0;

%e 0,0;

%e 0,0,0,4;

%e 0,0,0,4,4,0,4,32;

%e 0,0,0,4,4,0,4,32,12,0,4,28,24,4,40,176;

%e 0,0,0,4,4,0,4,32,12,0,4,28,24,4,40,176,28,0,4,28,24,4,40,172,72,4,36,144,116,48,256,832;

%Y Cf. A139250, A139251, A161207, A172311, A173530, A173531.

%K nonn

%O 0,8

%A _Omar E. Pol_, Oct 10 2010