

A273249


First differences of number of active (ON,black) cells in nth stage of growth of twodimensional cellular automaton defined by "Rule 617", based on the 5celled von Neumann neighborhood.


1



3, 17, 8, 43, 16, 64, 0, 112, 24, 112, 16, 160, 8, 184, 72, 288, 16, 264, 16, 240, 24, 328, 72, 424, 56, 432, 104, 504, 192, 608, 408, 768, 128, 664, 144, 616, 168, 800, 120, 700, 136, 724, 184, 888, 256, 868, 576, 1292, 352, 1004, 512, 1280
(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
Index entries for sequences related to cellular automata
Index to 2D 5Neighbor Cellular Automata
Index to Elementary Cellular Automata


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]]]+1)/2;
ca=Table[Table[Part[ca[[n]][[j]], Range[k+1n, k1+n]], {j, k+1n, k1+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. A273246.
Sequence in context: A093844 A273211 A273273 * A273303 A033467 A096475
Adjacent sequences: A273246 A273247 A273248 * A273250 A273251 A273252


KEYWORD

sign,easy


AUTHOR

Robert Price, May 18 2016


STATUS

approved



