# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a271166 Showing 1-1 of 1 %I A271166 #9 Jul 26 2024 21:16:36 %S A271166 1,6,15,47,60,164,189,381,430,746,787,1227,1336,1960,2029,2885,3066, %T A271166 4138,4323,5663,5872,7493,7741,9682,10018,12335,12623,15224,15664, %U A271166 18769,19142,22643,23211,27092,27760,32081,32770,37574,38279,43755,44708,50652,51481 %N A271166 Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 307", based on the 5-celled von Neumann neighborhood. %C A271166 Initialized with a single black (ON) cell at stage zero. %D A271166 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. %H A271166 Robert Price, Table of n, a(n) for n = 0..128 %H A271166 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 %H A271166 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton %H A271166 S. Wolfram, A New Kind of Science %H A271166 Index entries for sequences related to cellular automata %H A271166 Index to 2D 5-Neighbor Cellular Automata %H A271166 Index to Elementary Cellular Automata %t A271166 CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}]; %t A271166 code=307; stages=128; %t A271166 rule=IntegerDigits[code,2,10]; %t A271166 g=2*stages+1; (* Maximum size of grid *) %t A271166 a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *) %t A271166 ca=a; %t A271166 ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}]; %t A271166 PrependTo[ca,a]; %t A271166 (* Trim full grid to reflect growth by one cell at each stage *) %t A271166 k=(Length[ca[[1]]]+1)/2; %t A271166 ca=Table[Table[Part[ca[[n]][[j]],Range[k+1-n,k-1+n]],{j,k+1-n,k-1+n}],{n,1,k}]; %t A271166 on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *) %t A271166 Table[Total[Part[on,Range[1,i]]],{i,1,Length[on]}] (* Sum at each stage *) %Y A271166 Cf. A271164. %K A271166 nonn,easy %O A271166 0,2 %A A271166 _Robert Price_, Mar 31 2016 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE