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A273301
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 633", based on the 5-celled von Neumann neighborhood.
1
1, 5, 26, 55, 127, 215, 371, 531, 800, 1069, 1465, 1885, 2465, 3037, 3821, 4557, 5565, 6533, 7849, 9197, 10769, 12301, 14197, 15993, 18206, 20363, 22984, 25509, 28526, 31343, 34756, 37929, 41810, 45435, 49980, 54253, 59286, 64071, 69608, 74817, 80906, 86739
OFFSET
0,2
COMMENTS
Initialized with a single black (ON) cell at stage zero.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=633; stages=128;
rule=IntegerDigits[code, 2, 10];
g=2*stages+1; (* Maximum size of grid *)
a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca=a;
ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k=(Length[ca[[1]]]+1)/2;
ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}];
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)
CROSSREFS
Cf. A273299.
Sequence in context: A273210 A273272 A273248 * A042883 A273701 A273709
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 19 2016
STATUS
approved