The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A283349 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 617", based on the 5-celled von Neumann neighborhood. 4
 1, 0, 3, 1, 14, 6, 62, 30, 254, 126, 1022, 510, 4094, 2046, 16382, 8190, 65534, 32766, 262142, 131070, 1048574, 524286, 4194302, 2097150, 16777214, 8388606, 67108862, 33554430, 268435454, 134217726, 1073741822, 536870910, 4294967294, 2147483646, 17179869182 (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, Mar 06 2017: (Start) G.f.: (1 - x - x^2 + 2*x^3 + x^4 + 4*x^6) / ((1 - x)*(1 - 2*x)*(1 + 2*x)). a(n) = (-16 + 3*(-2)^n + 5*2^n) / 8 for n>3. a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) for n>4. (End) 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)/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. A282871, A283348, A283350. Sequence in context: A202039 A122689 A283402 * A204121 A079640 A079638 Adjacent sequences: A283346 A283347 A283348 * A283350 A283351 A283352 KEYWORD nonn,easy AUTHOR Robert Price, Mar 05 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 7 08:50 EST 2023. Contains 360115 sequences. (Running on oeis4.)