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!)
 A285647 Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 73", based on the 5-celled von Neumann neighborhood. 4
 1, 10, 1, 1100, 0, 111111, 0, 11111111, 0, 1111111111, 0, 111111111111, 0, 11111111111111, 0, 1111111111111111, 0, 111111111111111111, 0, 11111111111111111111, 0, 1111111111111111111111, 0, 111111111111111111111111, 0, 11111111111111111111111111, 0 (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..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, Apr 24 2017: (Start) G.f.: (1 + 10*x - 100*x^2 + 90*x^3 - x^4 + 1011*x^5 + 100*x^6 - 1100*x^7) / ((1 - x)*(1 + x)*(1 - 10*x)*(1 + 10*x)). a(n) = 0 for n>3 and even. a(n) = (10^(n+1) - 1)/9 for n>3 and odd. a(n) = 101*a(n-2) - 100*a(n-4) for n>7. (End) MATHEMATICA CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code = 73; 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]]] + 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. A285648, A285649, A285650. Sequence in context: A048176 A127616 A191549 * A287975 A288365 A288064 Adjacent sequences:  A285644 A285645 A285646 * A285648 A285649 A285650 KEYWORD nonn,easy AUTHOR Robert Price, Apr 23 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 November 28 13:47 EST 2021. Contains 349413 sequences. (Running on oeis4.)