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A268284 Period 15: repeat {18, 20, 28, 20, 20, 22, 18, 22, 20, 16, 12, 22, 18, 40, 18}. 1
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 (list; graph; refs; listen; history; text; internal format)
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, 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):

|. . . . . . . . . . . . . . . .| . . . . . . . . . . . . . . . .|

|. . . . . . . . . . . . . . . .| . . . . . . . . . . . . . . . .|

|. . . . o . . . . . . o . . . .| . . . o o . . . . . . o o . . .|

|. . . o o . . . . . . o o . . .| . . o . . o . . . . o . . o . .|

|. . o o o . . . . . . o o o . .| . . o . . o . . . . o . . o . .|

|. . . o o . . . . . . o o . . .| . . o . . o . . . . o . . o . .|

|. . . . o . . . . . . o . . . .| . . . o o . . . . . . o o . . .|

|. . . . . . . . . . . . . . . .| . . . . . . . . . . . . . . . .|

|. . . . . . . . . . . . . . . .| . . . . . . . . . . . . . . . .|

|(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: A295745 A255848 A072904 * A054279 A186781 A164711

Adjacent sequences:  A268281 A268282 A268283 * A268285 A268286 A268287

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Jan 30 2016

STATUS

approved

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Last modified March 23 04:46 EDT 2019. Contains 321422 sequences. (Running on oeis4.)