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%I #11 Feb 24 2021 02:48:18
%S 0,0,1,1,1,3,5,3,1,3,5,5,7,13,15,7,1,3,5,5,7,13,15,9,7,13,17,19,29,43,
%T 39,15,1,3,5,5,7,13,15,9,7,13,17,19,29,43,39,17,7,13,17,19,29,43,41,
%U 27,29,45,55,69,103,127,95,31
%N a(n) = A153003(n) - A153006(n).
%C The main entry for this sequence is the toothpick sequence A139250.
%H Jinyuan Wang, <a href="/A162777/b162777.txt">Rows n = 0..14 of triangle, flattened</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>
%F Observation: It appears that a(2^i) = 1, i > 0 and a(2^i-1) = 2^(i-1) - 1, i > 0.
%e If written as a triangle:
%e 0;
%e 0;
%e 1,1;
%e 1,3,5,3;
%e 1,3,5,5,7,13,15,7;
%e 1,3,5,5,7,13,15,9,7,13,17,19,29,43,39,15;
%e ...
%e Rows converge to A162779.
%Y Cf. A139250, A152980, A153003, A153004, A153006, A162779.
%K nonn,tabf
%O 0,6
%A _Omar E. Pol_, Jul 23 2009
%E More terms from _Jinyuan Wang_, Mar 15 2020
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