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%I #12 Feb 24 2021 02:48:18
%S 1,1,1,2,3,2,1,2,3,3,4,7,8,4,1,2,3,3,4,7,8,5,4,7,9,10,15,22,20,8,1,2,
%T 3,3,4,7,8,5,4,7,9,10,15,22,20,9,4,7,9,10,15,22,21,14,15,23,28,35,52,
%U 64,48,16,1,2,3,3,4,7,8,5,4,7,9,10,15,22,20,9,4,7,9,10,15,22,21,14,15,23
%N a(n) = A139251(n+2)/4 = A152968(n+1)/2.
%C Also, first differences of toothpick numbers A153000.
%H David Applegate, <a href="/A139250/a139250.anim.html">The movie version</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 G.f.: (1+x)*(Prod(1+x^(2^k-1)+2*x^(2^k),k=1..oo)-1)/(1+2*x). - _N. J. A. Sloane_, May 20 2009
%e If written as a triangle, begins:
%e .1,1;
%e .1,2,3,2;
%e .1,2,3,3,4,7,8,4;
%e .1,2,3,3,4,7,8,5,4,7,9,10,15,22,20,8;
%e ....
%e Rows converge to A152980.
%e It appears that row sums give A004171. [From _Omar E. Pol_, May 25 2010]
%Y Cf. toothpick sequence A139250.
%Y Cf. A139251, A139252, A139560, A152968, A152973.
%Y Cf. A152980, A152998, A153000, A153001, A153003, A153004, A153006.
%Y Cf. A004171. [From _Omar E. Pol_, May 25 2010]
%K nonn,easy
%O 1,4
%A _Omar E. Pol_, Dec 16 2008, Dec 20 2008
%E More terms from _Omar E. Pol_, Jul 26 2009
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