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%I A151692 #16 Oct 04 2024 20:51:01
%S A151692 1,0,0,1,1,0,0,1,1,0,1,2,1,0,0,1,1,0,1,2,1,0,1,2,1,1,3,3,1,0,0,1,1,0,
%T A151692 1,2,1,0,1,2,1,1,3,3,1,0,1,2,1,1,3,3,1,1,3,3,2,4,6,4,1,0,0,1,1,0,1,2,
%U A151692 1,0,1,2,1,1,3,3,1,0,1,2,1,1,3,3,1,1,3,3,2,4,6,4,1,0,1,2,1,1,3,3,1,1,3,3,2
%N A151692 G.f.: Product_{k>=2} (1 + x^(2^k-1) + x^(2^k)).
%H A151692 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 A151692 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 A151692 From _Omar E. Pol_, Jun 09 2009: (Start)
%e A151692 Triangle begins:
%e A151692 1;
%e A151692 0,0;
%e A151692 1,1,0,0;
%e A151692 1,1,0,1,2,1,0,0;
%e A151692 1,1,0,1,2,1,0,1,2,1,1,3,3,1,0,0;
%e A151692 1,1,0,1,2,1,0,1,2,1,1,3,3,1,0,1,2,1,1,3,3,1,1,3,3,2,4,6,4,1,0,0;
%e A151692 1,1,0,1,2,1,0,1,2,1,1,3,3,1,0,1,2,1,1,3,3,1,1,3,3,2,4,6,4,1,0,1,2,1,1,3,3,...
%e A151692 (End)
%Y A151692 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 A151692 Cf. A160573, A151552.
%Y A151692 Cf. A000079. - _Omar E. Pol_, Jun 09 2009
%K A151692 nonn
%O A151692 0,12
%A A151692 _N. J. A. Sloane_, Jun 04 2009