A254731 - OEIS

%I #14 Jun 16 2017 02:48:48

%S 4,8,24,20,32,68,48,72,116,88,104,140,188,160,284,272,268,320,372,352,

%T 496,488,524,608,556,628,692,820,764,808,864,976,1024,920,1032,1228,

%U 1188,1256,1408,1496,1488,1564,1584,1712,1752,1708,1888,2148,2040,2100,2308,2392,2544,2480,2760,2752,2764,3064,3020,2976,3516,3440,3560,3580,3804,3816,3916,4236,4492,4340,4516,4512,4984,4764,5004,4880,5116,5716,5540,5560,5564,5840,6200,6368,6280,6668,6880,6908,6960,7600,7388,7396,8028,7832,8332,8152,8268,8928,8708,9144

%N Number of ON cells in the even-rule cellular automaton after n steps with the Moore neighborhood (8 neighbors), with minimal nontrivial symmetric initial state (0,0), (0,1), (1,0), and (1,1) ON.

%C The rule turns a cell to ON at step n if an even, nonzero number of its eight neighbors were ON in the previous. For example, at n=2 the cell (0,0) is ON because the two neighbors (-1,0) and (0,-1) and no others were ON at the previous step.

%C It appears that whenever n is divisible by 3, there is a visible disjoint 2x2 square leading the automaton in each cardinal direction.

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%e For n=3, the configuration includes the initial four ON cells plus four other 2 X 2 squares in each cardinal direction.

%t m = 100; n = 2 m + 1;

%t A = Table[0, {p, 1, m}, {q, 1, n}, {z, 1, n}];

%t A[[1, m, m + 1]] = 1;

%t A[[1, m, m]] = 1;

%t A[[1, m + 1, m + 1]] = 1;

%t A[[1, m + 1, m]] = 1;

%t For[i = 2, i <= m, i++,

%t For[x = 2, x <= n - 1, x++,

%t   For[y = 2, y <= n - 1, y++,

%t    sum = A[[i - 1, x - 1, y - 1]] +

%t      A[[i - 1, x, y - 1]] +

%t      A[[i - 1, x + 1, y - 1]] +

%t      A[[i - 1, x - 1, y]] +

%t      A[[i - 1, x + 1, y]] +

%t      A[[i - 1, x - 1, y + 1]] +

%t      A[[i - 1, x, y + 1]] +

%t      A[[i - 1, x + 1, y + 1]];

%t    A[[i, x, y]] = If[sum > 0, 1 - Mod[sum, 2], 0];

%t    ]

%t   ]

%t ];

%t Table[Plus @@ Plus @@ A[[i, All, All]], {i, 1, m}]

%t (* _Kellen Myers_, Feb 07 2015 *)

%Y Cf. A160239.

%K nonn

%O 0,1

%A _Kellen Myers_, Feb 06 2015