OFFSET
0,2
COMMENTS
Initialized with a single black (ON) cell at stage zero.
Rules 46, 142 and 174 also generate this sequence.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
LINKS
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, Mar 08 2016: (Start)
a(n) = 4*3^(n-2)+4^n for n>1.
a(n) = 7*a(n-1)-12*a(n-2) for n>3.
G.f.: (1-2*x-3*x^2-4*x^3) / ((1-3*x)*(1-4*x)).
(End)
MATHEMATICA
rule=14; stages=300;
ca=CellularAutomaton[{rule, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, stages]; (* Start with single black cell *)
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Part[on, 2^Range[0, Log[2, stages]]] (* Extract relevant terms *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Robert Price, Mar 04 2016
EXTENSIONS
a(9)-a(15) from Lars Blomberg, Apr 12 2016
STATUS
approved