A169778 -id:A169778 - cp's OEIS frontend

A170905 Consider the hexagonal cellular automaton defined in A151723, A151724; a(n) = number of cells that go from OFF to ON at stage n, if we only look at a 60-degree wedge (including the two bounding edges).

0, 1, 2, 2, 4, 2, 4, 6, 8, 2, 4, 6, 10, 10, 8, 14, 16, 2, 4, 6, 10, 10, 10, 18, 26, 18, 8, 14, 24, 28, 20, 32, 32, 2, 4, 6, 10, 10, 10, 18, 26, 18, 10, 18, 30, 38, 34, 42, 58, 34, 8, 14, 24, 28, 28, 44, 68, 60, 28, 32, 56, 70, 50, 70, 64, 2, 4, 6, 10, 10, 10, 18, 26, 18, 10, 18, 30, 38, 34, 42

Offset: 0

N. J. A. Sloane, Jan 22 2010

			From _Omar E. Pol_, Feb 12 2013: (Start)
When written as a triangle starting from 1, the right border gives A000079 and row lengths give A011782.
1;
2;
2,4;
2,4,6,8;
2,4,6,10,10,8,14,16;
2,4,6,10,10,10,18,26,18,8,14,24,28,20,32,32;
2,4,6,10,10,10,18,26,18,10,18,30,38,34,42,58,34,8,14,24,28,28,44,68,60,28,32,56,70,50,70,64;
2,4,6,10,10,10,18,26,18,10,18,30,38,34,42,...
... (End)

N. J. A. Sloane, Table of n, a(n) for n = 0..1025
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, 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.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Cf. A151723, A151724, A170898, A169778, A169780 (partial sums).

a(n) = A170898(n-2) + 1 for n >= 2.

a(n) = 2*A169778(n) for n != 1.

A233782 a(n) = A233781(n+1)/2.

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 5, 5, 4, 7, 8, 1, 2, 3, 5, 5, 5, 9, 12, 9, 4, 7, 11, 13, 8, 15, 16, 1, 2, 3, 5, 5, 5, 9, 12, 9, 5, 9, 15, 19, 13, 21, 26, 17, 4, 7, 11, 13, 11, 21, 28, 25, 8, 15, 23, 29, 16, 31, 32, 1, 2, 3, 5, 5, 5, 9, 12, 9, 5, 9, 15, 19

Offset: 1

Omar E. Pol, Dec 17 2013

First 22 terms coincide with a(2)-a(23) of A169778.

			Written as an irregular triangle in which the row lengths is A000079 the sequence begins:
1;
1,2;
1,2,3,4;
1,2,3,5,5,4,7,8;
1,2,3,5,5,5,9,12,9,4,7,11,13,8,15,16;
1,2,3,5,5,5,9,12,9,5,9,15,19,13,21,26,17,4,7,11,13,11,21,28,25,8,15,23,29,16,31,32;

Right border gives A000079.

Cf. A139251, A169778, A220501, A220521, A231351, A233781, A233780.

cp's OEIS Frontend

A170905 Consider the hexagonal cellular automaton defined in A151723, A151724; a(n) = number of cells that go from OFF to ON at stage n, if we only look at a 60-degree wedge (including the two bounding edges).

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