OFFSET
0,4
COMMENTS
Initialized with a single black (ON) cell at stage zero.
Appears to be essentially the same as A277926. - R. J. Mathar, Nov 09 2016
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
FORMULA
Conjectures from Colin Barker, Nov 04 2016: (Start)
a(n) = 0 for n>1 and even.
a(n) = (10^(n+1)-1)/9 for n>1 and odd.
a(n) = 101*a(n-2)-100*a(n-4) for n>5.
G.f.: (1+x-101*x^2+1010*x^3+100*x^4-1000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)).
(End)
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=5; 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
KEYWORD
nonn,easy
AUTHOR
Robert Price, Nov 04 2016
STATUS
approved