A269567 Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 622", based on the 5-celled von Neumann neighborhood.

1, 6, 15, 36, 61, 98, 155, 224, 313, 414, 535, 668, 837, 1042, 1299, 1608, 1969, 2302, 2679, 3060, 3445, 3906, 4371, 4880, 5481, 6134, 6831, 7612, 8501, 9346, 10443, 11520, 12873, 14078, 15383, 16732, 18077, 19434, 20755, 22192, 23745, 25334, 26935, 28644

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, 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=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 *) Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}]

Crossrefs

Cf. A269522.

Sequence in context: A273390 A273451 A272928 * A253098 A272989 A273644

Adjacent sequences: A269564 A269565 A269566 * A269568 A269569 A269570

Keyword

nonn,easy

Author

Robert Price, Feb 29 2016

Status

approved