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%I #24 Feb 24 2021 02:48:19
%S 0,1,2,2,4,2,4,6,8,2,4,6,10,10,8,14,16,2,4,6,10,10,10,18,26,18,8,14,
%T 24,28,20,32,32,2,4,6,10,10,10,18,26,18,10,18,30,38,34,42,58,34,8,14,
%U 24,28,28,44,68,60,28,32,56,70,50,70,64,2,4,6,10,10,10,18,26,18,10,18,30,38,34,42
%N Consider the hexagonal cellular automaton defined in A151723, A151724; a(n) = number of cells that go from OFF to ON at stage n, if we only look at a 60-degree wedge (including the two bounding edges).
%H N. J. A. Sloane, <a href="/A170905/b170905.txt">Table of n, a(n) for n = 0..1025</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 a(n) = A170898(n-2) + 1 for n >= 2.
%F a(n) = 2*A169778(n) for n != 1.
%e From _Omar E. Pol_, Feb 12 2013: (Start)
%e When written as a triangle starting from 1, the right border gives A000079 and row lengths give A011782.
%e 1;
%e 2;
%e 2,4;
%e 2,4,6,8;
%e 2,4,6,10,10,8,14,16;
%e 2,4,6,10,10,10,18,26,18,8,14,24,28,20,32,32;
%e 2,4,6,10,10,10,18,26,18,10,18,30,38,34,42,58,34,8,14,24,28,28,44,68,60,28,32,56,70,50,70,64;
%e 2,4,6,10,10,10,18,26,18,10,18,30,38,34,42,...
%e ... (End)
%Y Cf. A151723, A151724, A170898, A169778, A169780 (partial sums).
%K nonn,tabf
%O 0,3
%A _N. J. A. Sloane_, Jan 22 2010
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