A269718 First differences 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.

4, 3, 12, -4, 28, -12, 56, -56, 60, -28, 120, -120, 120, -56, 240, -304, 124, -60, 248, -248, 248, -120, 496, -624, 248, -120, 496, -496, 496, -240, 992, -1376, 252, -124, 504, -504, 504, -248, 1008, -1264, 504, -248, 1008, -1008, 1008, -496, 2016, -2784

Offset

0,1

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..299

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[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)

Crossrefs

Cf. A269715.

Sequence in context: A270324 A271888 A271098 * A099377 A121844 A091512

Adjacent sequences: A269715 A269716 A269717 * A269719 A269720 A269721

Keyword

sign,easy

Author

Robert Price, Mar 04 2016

Status

approved