A246331 - OEIS

%I #20 Nov 05 2025 15:22:27

%S 1,9,25,49,89,113,161,233,345,369,417,489,609,681,825,1041,1369,1393,

%T 1441,1513,1633,1705,1849,2065,2401,2473,2617,2833,3193,3409,3841,

%U 4489,5465,5489,5537,5609,5729,5801,5945,6161,6497,6569,6713,6929,7289,7505,7937

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

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

%C This is a bisection of A147562.

%C 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.

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

%H N. J. A. Sloane, <a href="/A246331/a246331.pdf">Illustration of first 24 generations</a>

%H N. J. A. Sloane, <a href="https://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168, 2015

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%t 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 *)

%t ArrayPlot /@ CellularAutomaton[{465, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]

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

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Aug 30 2014