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%I #14 Feb 24 2021 02:48:18
%S 2,2,4,6,6,6,12,14,12,6,12,14,16,18,32,34,20,6,12,14,16,18,32,34,24,
%T 18,32,38,44,62,92,82,36,6,12,14,16,18,32,34,24,18,32,38,44,62,92,82,
%U 40,18,32,38,44,62
%N First differences of A160730.
%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 From _Nathaniel Johnston_, Mar 28 2011: (Start)
%F a(n) = 2*A168113(n)
%F a(2^(n+2) + 1) = 4(2^n + 1), n >= 1.
%F (End)
%e Placing the entries starting from a(4) in a triangle with rows that have length equal to powers of two gives:
%e 6, 6
%e 6, 12, 14, 12
%e 6, 12, 14, 16, 18, 32, 34, 20
%e 6, 12, 14, 16, 18, 32, 34, 24, 18, 32, 38, 44, 62, 92, 82, 36
%e ...
%e The rows of this triangle tend to 2*A168114.
%Y Cf. A139250, A139251, A160730, A160733, A160737, A160739, A160741.
%K nonn
%O 1,1
%A _Omar E. Pol_, May 25 2009
%E Terms after a(11) from _Nathaniel Johnston_, Mar 28 2011
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