login
A273272
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 625", based on the 5-celled von Neumann neighborhood.
1
1, 5, 26, 55, 127, 211, 352, 520, 780, 1069, 1438, 1822, 2350, 2914, 3598, 4326, 5274, 6250, 7414, 8646, 10058, 11474, 13071, 14776, 16840, 18953, 21314, 23630, 26318, 29094, 32107, 35096, 38588, 42181, 46050, 50167, 54620, 59104, 63897, 68766, 74095, 79611
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=625; 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. A273270.
Sequence in context: A083283 A049738 A273210 * A273248 A273301 A042883
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 18 2016
STATUS
approved