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 A151691 G.f.: Prod_{ k >= 1 } (1 + 2*x^(2^k-1) + x^(2^k)). 11

%I

%S 1,2,1,2,5,4,1,2,5,4,5,12,13,6,1,2,5,4,5,12,13,6,5,12,13,14,29,38,25,

%T 8,1,2,5,4,5,12,13,6,5,12,13,14,29,38,25,8,5,12,13,14,29,38,25,16,29,

%U 38,41,72,105,88,41,10,1,2,5,4,5,12,13,6,5,12,13,14,29,38,25,8,5,12,13,14,29

%N G.f.: Prod_{ k >= 1 } (1 + 2*x^(2^k-1) + x^(2^k)).

%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>

%e Contribution from _Omar E. Pol_, Jun 09 2009: (Start)

%e Triangle begins:

%e 1;

%e 2,1;

%e 2,5,4,1;

%e 2,5,4,5,12,13,6,1;

%e 2,5,4,5,12,13,6,5,12,13,14,29,38,25,8,1;

%e 2,5,4,5,12,13,6,5,12,13,14,29,38,25,8,5,12,13,14,29,38,25,16,29,38,41,72,...

%e (End)

%Y For generating functions of the form Prod_{k>=c} (1+a*x^(2^k-1)+b*x^2^k)) for the following values of (a,b,c) see: (1,1,0) A160573, (1,1,1) A151552, (1,1,2) A151692, (2,1,0) A151685, (2,1,1) A151691, (1,2,0) A151688 and A152980, (1,2,1) A151550, (2,2,0) A151693, (2,2,1) A151694

%Y Cf. A151685. See A151703 for another version with a simpler recurrence.

%Y Cf. A000079. [From _Omar E. Pol_, Jun 09 2009]

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jun 04 2009

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Last modified March 18 16:00 EDT 2019. Contains 321292 sequences. (Running on oeis4.)