A268284 - OEIS

%I #31 Sep 08 2022 08:46:15

%S 18,20,28,20,20,22,18,22,20,16,12,22,18,40,18,18,20,28,20,20,22,18,22,

%T 20,16,12,22,18,40,18,18,20,28,20,20,22,18,22,20,16,12,22,18,40,18,18,

%U 20,28,20,20,22,18,22,20,16,12,22,18,40,18,18,20,28,20,20,22,18,22,20,16,12,22,18,40,18

%N Period 15: repeat {18, 20, 28, 20, 20, 22, 18, 22, 20, 16, 12, 22, 18, 40, 18}.

%C Number of living cells periodic figure (oscillators: pentadecathlon (period 15)) in the Conway's Game of Life (rule B3/S23: see Graphical example in Links section).

%H Golly, <a href="http://golly.sourceforge.net">Cross-platform application for exploring Conway's Game of Life and other cellular automata</a>

%H Ilya Gutkovskiy, <a href="/A268284/a268284.txt">Graphical example (generation 0-15)</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GameofLife.html">Game of Life</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life">Conway's Game of Life</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Oscillator_(cellular_automaton)">Oscillator (cellular automaton)</a>

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

%F For k>=0:

%F a((30*k - 2*sin((Pi*k)/2) - 18*cos((Pi*k)/2) - cos(Pi*k) + 19)/8) = 18;

%F a((30*k + 10*sin((Pi*k)/2) + 18*cos((Pi*k)/2) + 3*cos(Pi*k) - 13)/8) = 20;

%F a(15*k + 2) = 28;

%F a(15*k + 9) = 16;

%F a(15*k + 10) = 12;

%F a(15*k + 13) = 40.

%e Start pattern (see Graphical example in Links section):

%e |. . . . . . . . . . . . . . . .| . . . . . . . . . . . . . . . .|

%e |. . . . . . . . . . . . . . . .| . . . . . . . . . . . . . . . .|

%e |. . . . o . . . . . . o . . . .| . . . o o . . . . . . o o . . .|

%e |. . . o o . . . . . . o o . . .| . . o . . o . . . . o . . o . .|

%e |. . o o o . . . . . . o o o . .| . . o . . o . . . . o . . o . .|

%e |. . . o o . . . . . . o o . . .| . . o . . o . . . . o . . o . .|

%e |. . . . o . . . . . . o . . . .| . . . o o . . . . . . o o . . .|

%e |. . . . . . . . . . . . . . . .| . . . . . . . . . . . . . . . .|

%e |. . . . . . . . . . . . . . . .| . . . . . . . . . . . . . . . .|

%e |(generation 0)                 |(generation 1), etc.            |

%t LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {18, 20, 28, 20, 20, 22, 18, 22, 20, 16, 12, 22, 18, 40, 18}, 80]

%o (Magma) &cat[[18,20,28,20,20,22,18,22,20,16,12,22,18,40,18]^^7]; // _Vincenzo Librandi_, Jan 30 2016

%o (PARI) a(n)=2*[9, 10, 14, 10, 10, 11, 9, 11, 10, 8, 6, 11, 9, 20, 9][n%15+1] \\ _Charles R Greathouse IV_, Jul 17 2016

%Y Cf. A061342, A152389, A179409.

%K nonn,easy

%O 0,1

%A _Ilya Gutkovskiy_, Jan 30 2016