This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A290528 Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 833", based on the 5-celled von Neumann neighborhood. 4
 1, 1, 5, 15, 3, 63, 7, 255, 15, 1023, 31, 4095, 63, 16383, 127, 65535, 255, 262143, 511, 1048575, 1023, 4194303, 2047, 16777215, 4095, 67108863, 8191, 268435455, 16383, 1073741823, 32767, 4294967295, 65535, 17179869183, 131071, 68719476735, 262143 (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, Aug 05 2017: (Start) G.f.: (1 - 2*x^2 + 10*x^3 - 28*x^4 + 48*x^6 - 32*x^7) / ((1 - x)*(1 - 2*x)*(1 + 2*x)*(1 - 2*x^2)). a(n) = 2^(n/2) - 1 for n>2 and even. a(n) = 2^(n+1) - 1 for n>2 and odd. a(n) = a(n-1) + 6*a(n-2) - 6*a(n-3) - 8*a(n-4) + 8*a(n-5) 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 = 833; 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[i, 2 * i - 1]], 10], {i, 1, stages - 1}] CROSSREFS Cf. A290525, A290526, A290527. Sequence in context: A306155 A082269 A107776 * A161202 A154353 A114332 Adjacent sequences:  A290525 A290526 A290527 * A290529 A290530 A290531 KEYWORD nonn,easy AUTHOR Robert Price, Aug 04 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 October 16 20:35 EDT 2019. Contains 328103 sequences. (Running on oeis4.)