%I
%S 1,1,2,3,3,3,6,7,6,3,6,7,8,9,16,17,10,3,6,7,8,9,16,17,12,9,16,19,22,
%T 31,46,41,18,3,6,7,8,9,16,17,12,9,16,19,22,31,46,41,20,9,16,19,22,31,
%U 46,43,30,31,48
%N First differences of A168112.
%C a(n) is the number of toothpicks added at the nth round in the toothpick structure of A168112.
%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), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)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+2) = 3, for i>0.
%F a(n) = A160731(n)/2. [From _Nathaniel Johnston_, Mar 28 2011]
%e If written as a triangle, begins:
%e 1;
%e 1;
%e 2;
%e 3,3;
%e 3,6,7,6;
%e 3,6,7,8,9,16,17,10;
%e 3,6,7,8,9,16,17,12,9,16,19,22,31,46,41,18;
%e Rows converge to A168114.
%Y Cf. A139250, A139251, A152978, A152980, A160407, A168112, A168114.
%K nonn,tabf
%O 1,3
%A _Omar E. Pol_, Dec 07 2009
%E Terms after a(34) from _Nathaniel Johnston_, Mar 28 2011
