A269522 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, 5, 9, 21, 25, 37, 57, 69, 89, 101, 121, 133, 169, 205, 257, 309, 361, 333, 377, 381, 385, 461, 465, 509, 601, 653, 697, 781, 889, 845, 1097, 1077, 1353, 1205, 1305, 1349, 1345, 1357, 1321, 1437, 1553, 1589, 1601, 1709, 1729, 1813, 1937, 2069, 2361, 2181

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

Robert Price, Diagrams of first 20 stages

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 *) Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

Crossrefs

Cf. A007483, A072272, A170878, A253908.

Sequence in context: A147562 A162795 A255366 * A169707 A256260 A256250

Adjacent sequences: A269519 A269520 A269521 * A269523 A269524 A269525

Keyword

nonn,easy

Author

Robert Price, Feb 28 2016

Status

approved