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%I #15 Feb 24 2021 02:48:18
%S 1,2,2,2,6,8,4,2,6,8,8,16,28,24,8,2,6,8,8,16,28,24,12,16,28,32,48,88,
%T 104,64,16,2,6,8,8,16,28,24,12,16,28,32,48,88,104,64,20,16,28,32,48,
%U 88,104,72,56,88,120,160,272,384,336,160,32,2,6,8,8,16,28,24,12,16,28,32,48,88
%N G.f.: Product_{k>=1} (1 + 2*x^(2^k-1) + 2*x^(2^k)).
%H 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 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 From _Omar E. Pol_, Jun 09 2009: (Start)
%e Triangle begins:
%e 1;
%e 2,2;
%e 2,6,8,4;
%e 2,6,8,8,16,28,24,8;
%e 2,6,8,8,16,28,24,12,16,28,32,48,88,104,64,16;
%e 2,6,8,8,16,28,24,12,16,28,32,48,88,104,64,20,16,28,32,48,88,104,72,56,88,...
%e (End)
%t CoefficientList[Series[Product[1+2x^(2^k-1)+2x^2^k,{k,10}],{x,0,80}],x] (* _Harvey P. Dale_, Oct 07 2020 *)
%Y For generating functions of the form Product_{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. A000079. - _Omar E. Pol_, Jun 09 2009
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jun 04 2009
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