login
A273248
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 617", based on the 5-celled von Neumann neighborhood.
1
1, 5, 26, 55, 127, 215, 367, 519, 783, 1071, 1471, 1887, 2463, 3047, 3815, 4511, 5495, 6495, 7759, 9039, 10559, 12103, 13975, 15775, 17999, 20167, 22767, 25263, 28263, 31071, 34487, 37495, 41271, 44919, 49231, 53399, 58183, 62799, 68215, 73511, 79507, 85367
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=617; 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. A273246.
Sequence in context: A049738 A273210 A273272 * A273301 A042883 A273701
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 18 2016
STATUS
approved