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A254731 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. 1
4, 8, 24, 20, 32, 68, 48, 72, 116, 88, 104, 140, 188, 160, 284, 272, 268, 320, 372, 352, 496, 488, 524, 608, 556, 628, 692, 820, 764, 808, 864, 976, 1024, 920, 1032, 1228, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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.

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

LINKS

Table of n, a(n) for n=0..99.

Index entries for sequences related to cellular automata

EXAMPLE

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

MATHEMATICA

m = 100; n = 2 m + 1;

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

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

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

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

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

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

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

  For[y = 2, y <= n - 1, y++,

   sum = A[[i - 1, x - 1, y - 1]] +

     A[[i - 1, x, y - 1]] +

     A[[i - 1, x + 1, y - 1]] +

     A[[i - 1, x - 1, y]] +

     A[[i - 1, x + 1, y]] +

     A[[i - 1, x - 1, y + 1]] +

     A[[i - 1, x, y + 1]] +

     A[[i - 1, x + 1, y + 1]];

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

   ]

  ]

];

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

(* Kellen Myers, Feb 07 2015 *)

CROSSREFS

Cf. A160239.

Sequence in context: A243557 A083504 A277291 * A291548 A212019 A075708

Adjacent sequences:  A254728 A254729 A254730 * A254732 A254733 A254734

KEYWORD

nonn

AUTHOR

Kellen Myers, Feb 06 2015

STATUS

approved

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Last modified February 18 15:08 EST 2018. Contains 299324 sequences. (Running on oeis4.)