This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A151694 #18 Oct 04 2024 20:51:11
%S A151694 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 A151694 104,64,16,2,6,8,8,16,28,24,12,16,28,32,48,88,104,64,20,16,28,32,48,
%U A151694 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 A151694 G.f.: Product_{k>=1} (1 + 2*x^(2^k-1) + 2*x^(2^k)).
%H A151694 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 A151694 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 A151694 From _Omar E. Pol_, Jun 09 2009: (Start)
%e A151694 Triangle begins:
%e A151694 1;
%e A151694 2,2;
%e A151694 2,6,8,4;
%e A151694 2,6,8,8,16,28,24,8;
%e A151694 2,6,8,8,16,28,24,12,16,28,32,48,88,104,64,16;
%e A151694 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 A151694 (End)
%t A151694 CoefficientList[Series[Product[1+2x^(2^k-1)+2x^2^k,{k,10}],{x,0,80}],x] (* _Harvey P. Dale_, Oct 07 2020 *)
%Y A151694 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 A151694 Cf. A000079. - _Omar E. Pol_, Jun 09 2009
%K A151694 nonn
%O A151694 0,2
%A A151694 _N. J. A. Sloane_, Jun 04 2009