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A273390
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 662", based on the 5-celled von Neumann neighborhood.
1
1, 6, 15, 36, 57, 102, 135, 216, 265, 374, 447, 628, 733, 974, 1063, 1360, 1541, 1942, 2079, 2528, 2817, 3402, 3631, 4268, 4649, 5470, 5775, 6668, 7145, 8234, 8595, 9796, 10365, 11810, 12267, 13828, 14529, 16354, 16903, 18832, 19649, 21874, 22531, 24888
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=662; 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. A273388.
Sequence in context: A272788 A273151 A320941 * A273451 A272928 A269567
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 21 2016
STATUS
approved