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 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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS Robert Price, Table of n, a(n) for n = 0..128 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton S. Wolfram, A New Kind of Science 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 Adjacent sequences:  A273245 A273246 A273247 * A273249 A273250 A273251 KEYWORD nonn,easy AUTHOR Robert Price, May 18 2016 STATUS approved

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Last modified March 23 18:13 EDT 2019. Contains 321433 sequences. (Running on oeis4.)