A268284 Period 15: repeat {18, 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, 18, 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, 18, 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

Offset

0,1

Comments

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).

Links

Table of n, a(n) for n=0..74.

Golly, Cross-platform application for exploring Conway's Game of Life and other cellular automata

Ilya Gutkovskiy, Graphical example (generation 0-15)

Eric Weisstein's World of Mathematics, Game of Life

Wikipedia, Conway's Game of Life

Wikipedia, Oscillator (cellular automaton)

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Formula

For k>=0:

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

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

a(15*k + 2) = 28;

a(15*k + 9) = 16;

a(15*k + 10) = 12;

a(15*k + 13) = 40.

Example

Start pattern (see Graphical example in Links section):
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|. . o o o . . . . . . o o o . .| . . o . . o . . . . o . . o . .|
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|. . . . . . . . . . . . . . . .| . . . . . . . . . . . . . . . .|
|(generation 0)                 |(generation 1), etc.            |

Mathematica

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]

Prog

(Magma) &cat[[18, 20, 28, 20, 20, 22, 18, 22, 20, 16, 12, 22, 18, 40, 18]^^7]; // Vincenzo Librandi, Jan 30 2016
(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

Crossrefs

Cf. A061342, A152389, A179409.

Sequence in context: A328934 A255848 A072904 * A367268 A054279 A186781

Adjacent sequences: A268281 A268282 A268283 * A268285 A268286 A268287

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Jan 30 2016

Status

approved