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

%I #30 Apr 10 2021 22:25:38

%S 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 79,150,243,216,81,2,7,12,13,20,45,54,31,20,45,62,79,150,243,216,85,

%U 20,45,62,79,150,243,224,133,150,259,344,537,936,1161,810,243,2,7,12,13,20,45

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

%C From _Omar E. Pol_, Apr 10 2021: (Start)

%C It appears that this is also an irregular triangle read by rows (see the example).

%C It appears that right border gives A000244.

%C It appears that row sums give A052934. (End)

%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_, Apr 10 2021: (Start)

%e Written as an irregular triangle in which row lengths are A000079 the sequence begins:

%e 1;

%e 2, 3;

%e 2, 7, 12, 9;

%e 2, 7, 12, 13, 20, 45, 54, 27;

%e 2, 7, 12, 13, 20, 45, 54, 31, 20, 45, 62, 79, 150, 243, 216, 81;

%e 2, 7, 12, 13, 20, 45, 54, 31, 20, 45, 62, 79, 150, 243, 216, 85, 20, 45, 62, ...

%e (End)

%t CoefficientList[Series[Product[1+2x^(2^k-1)+3x^2^k,{k,10}],{x,0,70}],x] (* _Harvey P. Dale_, Apr 09 2021 *)

%Y Cf. A000079, A000244, A052934, A275667.

%K nonn,tabf

%O 0,2

%A _N. J. A. Sloane_, Jan 02 2010

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)