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

%I A151555 #14 Feb 24 2021 02:48:18
%S A151555 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 A151555 33,41,50,72,96,80,33,5,10,13,15,20,32,33,23,20,33,41,50,72,96,81,39,
%U A151555 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 A151555 G.f.: (1 + 2x) * Product_{n>=1} (1 + x^(2^n-1) + 2*x^(2^n)).
%C A151555 From _Gary W. Adamson_, May 25 2009: (Start)
%C A151555 Convolved with A078008 signed (A151575) [1, 0, 2, -2, 6, -10, 22, -42, 86, -170, ...]
%C A151555 equals the toothpick sequence A153006: (1, 3, 6, 9, 13, 20, 28, ...). (End)
%C A151555 If A151550 is written as a triangle then the rows converge to this sequence. - _N. J. A. Sloane_, Jun 16 2009
%H A151555 N. J. A. Sloane, <a href="/A151555/b151555.txt">Table of n, a(n) for n = 0..16384</a>
%H A151555 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), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
%H A151555 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 A151555 From _Omar E. Pol_, Jun 19 2009: (Start)
%e A151555 May be written as a triangle:
%e A151555 1;
%e A151555 3;
%e A151555 4,5;
%e A151555 5,10,12,9;
%e A151555 5,10,13,15,20,32,32,17;
%e A151555 5,10,13,15,20,32,33,23,20,33,41,50,72,96,80,33;
%e A151555 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 A151555 (End)
%Y A151555 Cf. A139250, A151551, A151552, A151553, A151554, A151550, A152980, A153006.
%Y A151555 Cf. A078008. - _Gary W. Adamson_, May 25 2009
%K A151555 nonn
%O A151555 0,2
%A A151555 _N. J. A. Sloane_, May 20 2009