

A269716


Number of active (ON,black) cells at stage 2^n1 of the twodimensional cellular automaton defined by "Rule 22", based on the 5celled von Neumann neighborhood.


0



1, 5, 20, 88, 368, 1504, 6080, 24448, 98048, 392704, 1571840, 6289408, 25161728, 100655104, 402636800, 1610579968
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OFFSET

0,2


COMMENTS

Initialized with a single black (ON) cell at stage zero.
Appears to coincide with A093357 after the second term.  R. J. Mathar, Mar 09 2016


REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.


LINKS

Table of n, a(n) for n=0..15.
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


FORMULA

Conjectures from Colin Barker, Mar 08 2016: (Start)
a(n) = 2^(n1)*(3*2^n2) for n>1.
a(n) = 6*a(n1)8*a(n2) for n>3.
G.f.: (1+2*x)*(13*x+4*x^2) / ((12*x)*(14*x)).
(End)


MATHEMATICA

rule=22; 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

Cf. A269715.
Sequence in context: A219672 A011966 A271096 * A192249 A017966 A196532
Adjacent sequences: A269713 A269714 A269715 * A269717 A269718 A269719


KEYWORD

nonn,more


AUTHOR

Robert Price, Mar 04 2016


EXTENSIONS

a(9)a(15) from Lars Blomberg, Apr 15 2016


STATUS

approved



