

A269708


Number of active (ON,black) cells at stage 2^n1 of the twodimensional cellular automaton defined by "Rule 14", based on the 5celled von Neumann neighborhood.


0



1, 5, 20, 76, 292, 1132, 4420, 17356, 68452, 270892, 1074820, 4273036, 17013412, 67817452, 270561220, 1080119116
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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



FORMULA

a(n) = 4*3^(n2)+4^n for n>1.
a(n) = 7*a(n1)12*a(n2) for n>3.
G.f.: (12*x3*x^24*x^3) / ((13*x)*(14*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



EXTENSIONS



STATUS

approved



