%I #16 Feb 24 2021 02:48:18

%S 0,1,13,25,109,121,205,385,805,817,901,1081,1645,2185,2605,3721,5749,

%T 5857,5941,6121,6685,7225,7789,9289,12565,14401,14821,15937,18877,

%U 23257,25981,32233,42445,43729,44101,44521

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

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

%C We start with a single ON cell at the origin.

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

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

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

%H Nathaniel Johnston, <a href="/A151776/b151776.txt">Table of n, a(n) for n = 0..68</a>

%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]

%H Nathaniel Johnston, <a href="/A151776/a151776.c.txt">C script</a>

%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/Fa#fcc">Index entries for sequences related to f.c.c. lattice</a>

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

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jun 24 2009

%E Terms after a(30) from _Nathaniel Johnston_, Mar 27 2011