A269755 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 30", based on the 5-celled von Neumann neighborhood.

1, 6, 18, 34, 70, 94, 154, 198, 314, 358, 486, 606, 806, 950, 1210, 1454, 1750, 2018, 2386, 2778, 3166, 3550, 4042, 4634, 5198, 5702, 6458, 7250, 8006, 8718, 9610, 10670, 11506, 12382, 13534, 14834, 16058, 17150, 18462, 20150, 21546, 22858, 24642, 26618

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=30; 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. A269753.

Sequence in context: A323148 A181510 A301715 * A270135 A038343 A271123

Adjacent sequences: A269752 A269753 A269754 * A269756 A269757 A269758

Keyword

nonn,easy

Author

Robert Price, Mar 04 2016

Status

approved