A151776 Number of ON states after n generations of cellular automaton based on f.c.c. lattice with each cell adjacent to its twelve neighbors.

0, 1, 13, 25, 109, 121, 205, 385, 805, 817, 901, 1081, 1645, 2185, 2605, 3721, 5749, 5857, 5941, 6121, 6685, 7225, 7789, 9289, 12565, 14401, 14821, 15937, 18877, 23257, 25981, 32233, 42445, 43729, 44101, 44521

Offset: 0

Author

N. J. A. Sloane, Jun 24 2009

Keywords

• nonn

Comments

We take the f.c.c. lattice to consist of the points (X,Y,Z) of Z^3 with X+Y+Z even.

We start with a single ON cell at the origin.

A cell is turned ON if exactly one of its twelve neighbors is ON. An ON cell remains ON forever.

Analog of A147562, which is corresponding sequence for the square lattice Z^2.

If we just look at what happens in the (X,Y)-plane, we get A147552 and A151836.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..68
• 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.]
• Nathaniel Johnston, C script
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to f.c.c. lattice

Crossrefs

Cf. A151777, A151778, A147562, A151725, A139250.

Extensions

Terms after a(30) from Nathaniel Johnston, Mar 27 2011