A220521 - OEIS

%I #31 Apr 29 2020 16:10:01

%S 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 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 36,48,56,64,74,76,30,44,72,88,60,64,64,4,4,8,12

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

%C From _Omar E. Pol_, Apr 26 2020: (Start)

%C The cellular automaton described in A220520 has word "ab", so the structure of this triangle is as follows:

%C a,b;

%C a,b;

%C a,b,a,b;

%C a,b,a,b,a,b,a,b;

%C a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b;

%C ...

%C 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 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 For further information about the "word" of a cellular automaton see A296612. (End)

%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>

%H <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>

%e Written as an irregular triangle the sequence begins:

%e 1,2;

%e 4,4;

%e 4,4,8,8;

%e 4,4,8,12,16,12,16,16;

%e 4,4,8,12,16,20,24,26,24,12,20,32,40,28,32,32;

%e 4,4,8,12,16,20,24,26,24,20,32,44,64,52,48,54,40,12,20,...

%e Triangle reformatted by _Omar E. Pol_, Apr 26 2020

%Y First differences of A220520.

%Y First differs from A194441 at a(14).

%Y Columns 1-3: A123932, A040002, A010731.

%Y Cf. A139250, A139251, A194443, A220501, A220523, A296612.

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Dec 15 2012

%E 0 removed and offset changed by _Omar E. Pol_, Apr 26 2020