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

0,3

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. [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

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.
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)

Crossrefs

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

Sequence in context: A233765 A233781 A233971 * A233761 A035096 A066675

Adjacent sequences: A170902 A170903 A170904 * A170906 A170907 A170908

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jan 22 2010

Status

approved