A269812 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 33", based on the 5-celled von Neumann neighborhood.

1, 5, 10, 42, 51, 143, 164, 328, 353, 641, 678, 1098, 1155, 1727, 1812, 2544, 2633, 3617, 3718, 4962, 5083, 6603, 6768, 8540, 8749, 10833, 11102, 13514, 13795, 16543, 16892, 19976, 20329, 23921, 24286, 28394, 28779, 33419, 33848, 38996, 39469, 45181, 45730

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..128

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=33; 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. A269810.

Sequence in context: A321307 A270288 A271805 * A271127 A270016 A271162

Adjacent sequences: A269809 A269810 A269811 * A269813 A269814 A269815

Keyword

nonn,easy

Author

Robert Price, Mar 05 2016

Status

approved