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A273306
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 637", based on the 5-celled von Neumann neighborhood.
1
1, 9, 29, 74, 135, 247, 383, 595, 819, 1160, 1509, 2001, 2525, 3209, 3917, 4809, 5701, 6841, 7997, 9429, 10877, 12633, 14349, 16461, 18469, 20957, 23293, 26185, 28917, 32293, 35585, 39370, 42811, 47080, 51101, 55890, 60423, 65784, 70889, 76866, 82403, 88948
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=637; 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. A273304.
Sequence in context: A273243 A273297 A273268 * A318742 A024922 A193004
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 19 2016
STATUS
approved