A269717 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 22", based on the 5-celled von Neumann neighborhood.

1, 6, 14, 34, 50, 94, 126, 214, 246, 338, 402, 586, 650, 834, 962, 1330, 1394, 1582, 1710, 2086, 2214, 2590, 2846, 3598, 3726, 4102, 4358, 5110, 5366, 6118, 6630, 8134, 8262, 8642, 8898, 9658, 9914, 10674, 11186, 12706, 12962, 13722, 14234, 15754, 16266

Offset

0,2

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

Robert Price, Table of n, a(n) for n = 0..300

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 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

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 *)
Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)

Crossrefs

Cf. A269715.

Sequence in context: A074981 A066510 A279730 * A271097 A269709 A270093

Adjacent sequences: A269714 A269715 A269716 * A269718 A269719 A269720

Keyword

nonn,easy

Author

Robert Price, Mar 04 2016

Status

approved