The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A273147 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 597", based on the 5-celled von Neumann neighborhood. 1
 7, 12, 21, 16, 47, 12, 77, 0, 119, -20, 165, -48, 223, -84, 285, -128, 359, -180, 437, -240, 527, -308, 621, -384, 727, -468, 837, -560, 959, -660, 1085, -768, 1223, -884, 1365, -1008, 1519, -1140, 1677, -1280, 1847, -1428, 2021, -1584, 2207, -1748, 2397 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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..127 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 Conjectures from Colin Barker, May 16 2016: (Start) a(n) = -a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5)-a(n-6)-a(n-7) for n>6. G.f.: (7+19*x+26*x^2+18*x^3+23*x^4+3*x^5) / ((1-x)^2*(1+x)^3*(1+x^2)). (End) MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=597; 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}]; on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *) Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *) CROSSREFS Cf. A273144. Sequence in context: A025006 A189321 A273072 * A272845 A272927 A272946 Adjacent sequences:  A273144 A273145 A273146 * A273148 A273149 A273150 KEYWORD sign,easy AUTHOR Robert Price, May 16 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 17 05:07 EDT 2022. Contains 356184 sequences. (Running on oeis4.)