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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

FORMULA

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

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

EXAMPLE

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.

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;