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A170842 G.f.: Product_{k>=1} (1 + 2x^(2^k-1) + 3x^(2^k)).

%I A170842 #34 Aug 16 2024 19:04:30
%S A170842 1,2,3,2,7,12,9,2,7,12,13,20,45,54,27,2,7,12,13,20,45,54,31,20,45,62,
%T A170842 79,150,243,216,81,2,7,12,13,20,45,54,31,20,45,62,79,150,243,216,85,
%U A170842 20,45,62,79,150,243,224,133,150,259,344,537,936,1161,810,243,2,7,12,13,20,45
%N A170842 G.f.: Product_{k>=1} (1 + 2x^(2^k-1) + 3x^(2^k)).
%C A170842 From _Omar E. Pol_, Apr 10 2021: (Start)
%C A170842 It appears that this is also an irregular triangle read by rows (see the example).
%C A170842 It appears that right border gives A000244.
%C A170842 It appears that row sums give A052934. (End)
%H A170842 John Tyler Rascoe, <a href="/A170842/b170842.txt">Table of n, a(n) for n = 0..8192</a>
%H A170842 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 A170842 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 A170842 From _Omar E. Pol_, Apr 10 2021: (Start)
%e A170842 Written as an irregular triangle in which row lengths are A000079 the sequence begins:
%e A170842 1;
%e A170842 2, 3;
%e A170842 2, 7, 12, 9;
%e A170842 2, 7, 12, 13, 20, 45, 54, 27;
%e A170842 2, 7, 12, 13, 20, 45, 54, 31, 20, 45, 62, 79, 150, 243, 216, 81;
%e A170842 2, 7, 12, 13, 20, 45, 54, 31, 20, 45, 62, 79, 150, 243, 216, 85, 20, 45, 62, ...
%e A170842 (End)
%t A170842 CoefficientList[Series[Product[1+2x^(2^k-1)+3x^2^k,{k,10}],{x,0,70}],x] (* _Harvey P. Dale_, Apr 09 2021 *)
%o A170842 (PARI)
%o A170842 D_x(N) = {my( x='x+O('x^N));Vec(prod(k=1,logint(N,2)+1,(1+2*x^(2^k-1)+3*x^(2^k))))}
%o A170842 D_x((2^6)+1) \\ _John Tyler Rascoe_, Aug 16 2024
%Y A170842 Cf. A000079, A000244, A052934, A275667.
%K A170842 nonn,tabf
%O A170842 0,2
%A A170842 _N. J. A. Sloane_, Jan 02 2010