The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A271904 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 427", based on the 5-celled von Neumann neighborhood. 1
 1, 6, 19, 51, 88, 177, 257, 402, 515, 807, 976, 1333, 1577, 2158, 2451, 3139, 3536, 4505, 4977, 6082, 6667, 8143, 8816, 10437, 11265, 13334, 14243, 16499, 17592, 20353, 21553, 24530, 25923, 29495, 31008, 34805, 36553, 41022, 42883, 47619, 49744, 55209, 57473 (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 FORMULA Empirical g.f.: (1 +6*x +18*x^2 +44*x^3 +61*x^4 +96*x^5 +88*x^6 +68*x^7 +7*x^8 +26*x^9 +6*x^10 -5*x^12) / ((1 -x)^4*(1 +x)^3*(1 +x^2)^2*(1 +x +x^2)). - Colin Barker, Apr 21 2016 MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=427; 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)/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. A271902. Sequence in context: A269059 A324218 A229731 * A272541 A273142 A273173 Adjacent sequences:  A271901 A271902 A271903 * A271905 A271906 A271907 KEYWORD nonn,easy AUTHOR Robert Price, Apr 20 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 30 21:33 EDT 2021. Contains 346365 sequences. (Running on oeis4.)