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!)
 A280369 Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 259", based on the 5-celled von Neumann neighborhood. 4
 1, 1, 3, 8, 3, 56, 3, 248, 3, 1016, 3, 4088, 3, 16376, 3, 65528, 3, 262136, 3, 1048568, 3, 4194296, 3, 16777208, 3, 67108856, 3, 268435448, 3, 1073741816, 3, 4294967288, 3, 17179869176, 3, 68719476728, 3, 274877906936, 3, 1099511627768, 3, 4398046511096, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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..126 Robert Price, Diagrams of first 20 stages 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 Wolfram Research, Wolfram Atlas of Simple Programs FORMULA Conjectures from Colin Barker, Jan 01 2017: (Start) a(n) = 3 for n>1 and even. a(n) = 2^(n+1) - 8 for n>1 and odd. a(n) = 5*a(n-2) - 4*a(n-4) for n>5. G.f.: (1 + x - 2*x^2 + 3*x^3 - 8*x^4 + 20*x^5) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)). (End) MATHEMATICA CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code = 259; 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}]; Table[FromDigits[Part[ca[[i]] [[i]], Range[1, i]], 2], {i, 1, stages - 1}] CROSSREFS Cf. A280367, A280368, A280370. Sequence in context: A046970 A322360 A058936 * A280979 A281045 A002017 Adjacent sequences:  A280366 A280367 A280368 * A280370 A280371 A280372 KEYWORD nonn,easy AUTHOR Robert Price, Jan 01 2017 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 May 8 02:26 EDT 2021. Contains 343652 sequences. (Running on oeis4.)