cp's OEIS Frontend

A220521 Number of toothpicks or D-toothpicks added at n-th stage in the toothpick structure of A220520.

%I A220521 #31 Apr 29 2020 16:10:01
%S A220521 1,2,4,4,4,4,8,8,4,4,8,12,16,12,16,16,4,4,8,12,16,20,24,26,24,12,20,
%T A220521 32,40,28,32,32,4,4,8,12,16,20,24,26,24,20,32,44,64,52,48,54,40,12,20,
%U A220521 36,48,56,64,74,76,30,44,72,88,60,64,64,4,4,8,12
%N A220521 Number of toothpicks or D-toothpicks added at n-th stage in the toothpick structure of A220520.
%C A220521 From _Omar E. Pol_, Apr 26 2020: (Start)
%C A220521 The cellular automaton described in A220520 has word "ab", so the structure of this triangle is as follows:
%C A220521 a,b;
%C A220521 a,b;
%C A220521 a,b,a,b;
%C A220521 a,b,a,b,a,b,a,b;
%C A220521 a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b;
%C A220521 ...
%C A220521 The row lengths are the terms of A011782 multiplied by 2, equaling the column 2 of the square array A296612: 2, 2, 4, 8, 16, ...
%C A220521 This arrangement has the property that the odd-indexed columns (a) contain numbers of the toothpicks of length 1, and the even-indexed columns (b) contain numbers of the D-toothpicks.
%C A220521 For further information about the "word" of a cellular automaton see A296612. (End)
%H A220521 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 A220521 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%e A220521 Written as an irregular triangle the sequence begins:
%e A220521 1,2;
%e A220521 4,4;
%e A220521 4,4,8,8;
%e A220521 4,4,8,12,16,12,16,16;
%e A220521 4,4,8,12,16,20,24,26,24,12,20,32,40,28,32,32;
%e A220521 4,4,8,12,16,20,24,26,24,20,32,44,64,52,48,54,40,12,20,...
%e A220521 Triangle reformatted by _Omar E. Pol_, Apr 26 2020
%Y A220521 First differences of A220520.
%Y A220521 First differs from A194441 at a(14).
%Y A220521 Columns 1-3: A123932, A040002, A010731.
%Y A220521 Cf. A139250, A139251, A194443, A220501, A220523, A296612.
%K A220521 nonn,tabf
%O A220521 1,2
%A A220521 _Omar E. Pol_, Dec 15 2012
%E A220521 0 removed and offset changed by _Omar E. Pol_, Apr 26 2020