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A323651 Number of elements added at n-th stage to the toothpick structure of A323650.

%I A323651 #28 Apr 11 2019 22:49:20
%S A323651 1,2,4,8,4,8,12,24,4,8,12,24,12,24,36,72,4,8,12,24,12,24,36,72,12,24,
%T A323651 36,72,36,72,108,216,4,8,12,24,12,24,36,72,12,24,36,72,36,72,108,216,
%U A323651 12,24,36,72,36,72,108,216,36,72,108,216,108,216,324,648,4,8,12,24,12,24,36,72,12,24,36,72,36,72,108,216
%N A323651 Number of elements added at n-th stage to the toothpick structure of A323650.
%C A323651 The odd-indexed terms (a bisection) gives A147582, the first differences of A147562 (Ulam-Warburton cellular automaton).
%C A323651 The even-indexed terms (a bisection) gives A147582 multiplied by 2.
%C A323651 The word of this cellular automaton is "ab", so the structure of the irregular triangle is as shown below:
%C A323651 a,b;
%C A323651 a,b;
%C A323651 a,b,a,b;
%C A323651 a,b,a,b,a,b,a,b;
%C A323651 a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b;
%C A323651 ...
%C A323651 Row lengths are the terms of A011782 multiplied by 2, also the column 2 of A296612.
%C A323651 Columns "a" contain numbers of I-toothpicks. Columns "b" contain numbers of V-toothpicks. See the example.
%C A323651 For further information about the word of cellular automata see A296612.
%H A323651 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>
%H A323651 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A323651 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%F A323651 a(2n-1) = A147582(n).
%F A323651 a(2n) = 2*A147582(n).
%F A323651 a(n) = 4*A323641(n-2), n >= 3.
%e A323651 Written as an irregular triangle the sequence begins:
%e A323651 1,2;
%e A323651 4,8;
%e A323651 4,8,12,24;
%e A323651 4,8,12,24,12,24,36,72;
%e A323651 4,8,12,24,12,24,36,72,12,24,36,72,36,72,108,216;
%e A323651 4,8,12,24,12,24,36,72,12,24,36,72,36,72,108,216,12,24,36,72,36,72,108,216,...
%e A323651 ...
%Y A323651 First differences of A323650.
%Y A323651 Cf. A011782, A139250, A139251, A147562, A147582, A160120, A160121, A161206, A161207, A296612, A323641, A323642, A323649.
%Y A323651 For other hybrid cellular automata, see A194701, A194271, A220501, A290221, A294021, A294981.
%K A323651 nonn
%O A323651 1,2
%A A323651 _Omar E. Pol_, Feb 04 2019