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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, 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): |. . . . . . . . . . . . . . . .| . . . . . . . . . . . . . . . .| |. . . . . . . . . . . . . . . .| . . . . . . . . . . . . . . . .| |. . . . 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: 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

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Last modified February 22 08:27 EST 2024. Contains 370240 sequences. (Running on oeis4.)