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A152968 a(n) = A139251(n+1)/2. 17

%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), 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 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^r-1) = 2^(r-1). - _N. J. A. Sloane_, Jun 03 2009, Jul 16 2009

%F G.f.: x*(Prod(1+x^(2^k-1)+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

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)