A269566 Number of active (ON, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 622", based on the 5-celled von Neumann neighborhood.

1, 5, 21, 69, 309, 1077, 4661, 19173, 74917, 310285, 1234813, 4909789, 19434725, 76878941, 304281693, 1205650205

Offset: 0

Author

Robert Price, Feb 29 2016

Keywords

• nonn
• more

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

• N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 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 5-Neighbor Cellular Automata

Crossrefs

Cf. A269522.

Programs

Mathematica

rule=622; 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]]]

Extensions

a(9)-a(15) from Lars Blomberg, Jul 16 2016