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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
Eric Weisstein's World of Mathematics, Game of Life
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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|(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
Sequence in context: A328934 A255848 A072904 * A367268 A054279 A186781
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.)