A246331 Total number of ON cells at stage 2n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 465".

1, 9, 25, 49, 89, 113, 161, 233, 345, 369, 417, 489, 609, 681, 825, 1041, 1369, 1393, 1441, 1513, 1633, 1705, 1849, 2065, 2401, 2473, 2617, 2833, 3193, 3409, 3841, 4489, 5465, 5489, 5537, 5609, 5729, 5801, 5945, 6161, 6497, 6569, 6713, 6929, 7289, 7505, 7937

Offset

0,2

Comments

The number of ON cells at stage 2n+1 is infinite.

This is a bisection of A147562.

The sequence b(n) defined by b(n) = number of ON cells at stage n if n is even, b(n) = number of OFF cells at stage n if n is odd coincides with A147562, and has a simple formula.

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; pp. 173-175.

Links

Table of n, a(n) for n=0..46.

N. J. A. Sloane, Illustration of first 24 generations

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015

Index entries for sequences related to cellular automata

Mathematica

Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 465, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 130]] (* then take every other term *)
ArrayPlot /@ CellularAutomaton[{465, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

Crossrefs

Cf. A147562, A169699, A246316, A246318, A246325, A246326, ...

Sequence in context: A331587 A192775 A318737 * A141768 A339126 A176970

Adjacent sequences: A246328 A246329 A246330 * A246332 A246333 A246334

Keyword

nonn

Author

N. J. A. Sloane, Aug 30 2014

Status

approved