%I
%S 1,2,2,2,4,6,4,2,4,6,6,8,14,16,8,2,4,6,6,8,14,16,10,8,14,18,20,30,44,
%T 40,16,2,4,6,6,8,14,16,10,8,14,18,20,30,44,40,18,8,14,18,20,30,44,42,
%U 28,30,46,56,70,104,128,96,32,2
%N a(n) = A139251(n+1)/2.
%C Also, first differences of toothpicks numbers A152998. [From _Omar E. Pol_, Jan 02 2009]
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="http://neilsloane.com/doc/tooth.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 Write n = 2^i +j, 0 <= j < 2^i; then a(n) = Sum_k 2^(wt(j+k)k)*binomial(wt(j+k),k). except that a(2^r1) = 2^(r1).  _N. J. A. Sloane_, Jun 03 2009, Jul 16 2009
%F G.f.: x*(Prod(1+x^(2^k1)+2*x^(2^k),k=0..oo)1)/(1+2*x).  _N. J. A. Sloane_, Jun 05 2009
%e Triangle begins:
%e .1;
%e .2,2;
%e .2,4,6,4;
%e .2,4,6,6,8,14,16,8;
%e .2,4,6,6,8,14,16,10,8,14,18,20,30,44,40,16;
%e ....
%e Rows approach A151688.  _N. J. A. Sloane_, Jun 03 2009
%Y Cf. A139250, A139251, A139252, A152978, A152980, A153006, A152998.
%K nonn
%O 1,2
%A _Omar E. Pol_, Dec 16 2008, Dec 20 2008
