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A151555 G.f.: (1 + 2x ) * Prod_{ n >= 1} (1 + x^(2^n-1) + 2*x^(2^n)). 5

%I

%S 1,3,4,5,5,10,12,9,5,10,13,15,20,32,32,17,5,10,13,15,20,32,33,23,20,

%T 33,41,50,72,96,80,33,5,10,13,15,20,32,33,23,20,33,41,50,72,96,81,39,

%U 20,33,41,50,72,97,89,66,73,107,132,172,240,272,192,65,5,10,13,15,20,32,33,23

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

%C Contribution from _Gary W. Adamson_, May 25 2009: (Start)

%C Convolved with A078008 signed (A151575) [1, 0, 2, -2, 6, -10, 22, -42, 86, -170,...]

%C equals the toothpick sequence A153006: (1, 3, 6, 9, 13, 20, 28,...). (End)

%C If A151550 is written as a triangle then the rows converge to this sequence. - _N. J. A. Sloane_, Jun 16 2009

%H N. J. A. Sloane, <a href="/A151555/b151555.txt">Table of n, a(n) for n = 0..16384</a>

%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 19 2009: (Start)

%e May be written as a triangle:

%e 1;

%e 3;

%e 4,5;

%e 5,10,12,9;

%e 5,10,13,15,20,32,32,17;

%e 5,10,13,15,20,32,33,23,20,33,41,50,72,96,80,33;

%e 5,10,13,15,20,32,33,23,20,33,41,50,72,96,81,39,20,33,41,50,72,97,89,66,73,...

%e (End)

%Y Cf. A139250, A151551, A151552, A151553, A151554, A151550, A152980, A153006.

%Y Cf. A078008 [From _Gary W. Adamson_, May 25 2009]

%K nonn

%O 0,2

%A _N. J. A. Sloane_, May 20 2009

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Last modified August 11 00:32 EDT 2020. Contains 336403 sequences. (Running on oeis4.)