A086993 -id:A086993 - cp's OEIS frontend

A089520 In Conway's Game of Life, the number of steps it takes for an n X n square, in which all the cells are in the "on" state, to die out or start to cycle, or -1 if there is no cycle.

1, 0, 5, 4, 11, 5, 5, 6, 16, 17, 32, 9, 18, 9, 22, 11, 33, 17, 20, 12, 26, 13, 48, 15, 46, 26, 295, 45, 154, 38, 62, 309, 38, 87, 78, 53, 96, 150, 641, 69, 82, 265, 216, 70, 70, 70, 120, 401, 107, 78, 70, 351, 318, 109, 297, 95, 122, -1, -1, 85, 232, 294, 127

Offset: 1

Anne M. Donovan (anned3005(AT)aol.com), Nov 05 2003

sign

The -1 terms for n = 58, 59, 80, 92, 95, 96, 98, 99, 100 correspond to starting n x n squares that produce 8 gliders (16 for n = 99) that go off to infinity, hence never reaching a cycle. - Michael S. Branicky, Jul 06 2022

			a(1) = 1 since a single cell is switched off on step 1.
a(2) = 0 since a block is cyclic to start with: 0th = 1st generation.
a(3) = 5 since a cycle starts there: 5th = 7th generation.

Michael S. Branicky, Table of n, a(n) for n = 1..100
Michael S. Branicky, Python program and utilities.
D. Griffeath, Life32 by Johan Bontes.
Nathaniel Johnston, ConwayLife.com.
S. Silver, Life Lexicon.

Cf. A019473, A086993.

More terms from John W. Layman, Nov 07 2003
39 more terms from Rick L. Shepherd, Jun 04 2004
Name edited, a(58) and a(59) changed, and a(61) and beyond from Michael S. Branicky, Jul 06 2022

A086973 Period of oscillator reached starting with a segment of n consecutive live cells and applying the LongLife 2D rule (see comment).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 2, 2, 6, 6, 8, 8, 14, 14, 2, 2, 28, 28, 6, 6, 62, 62, 16, 16, 126, 126, 28, 28, 112, 60, 6, 6, 10, 30, 2, 56, 2640, 2, 4, 6, 2, 4, 4, 4, 2, 6, 2, 2, 2, 2, 6, 14, 6, 6, 2, 6, 102, 6, 2, 4, 18, 42, 2, 2, 102, 12, 42, 2, 18, 12, 6

Offset: 1

Benoit Cloitre, Sep 22 2003

nonn

LongLife rule : birth occurs if dead cell has 3,4 or 5 neighbors. Survival occurs if live cell has 5 neighbors. (Sequence computed using LifeLab for mac).

Rémy Sigrist, PARI program
Eric Weisstein's World of Mathematics, Game of Life.

Cf. A086993 (pre-periodic steps).

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More terms from Rémy Sigrist, Sep 07 2022

A086992 Product of nonzero digits in n-th row of Pascal's triangle.

Original entry on oeis.org

1, 1, 2, 9, 96, 25, 1800, 44100, 103219200, 3869835264, 128000, 104976000000, 3071875232563200, 7050692013745766400, 626913312768, 332150625000000000000, 1292730125539029811200

Offset: 1

Jason Earls, Jul 29 2003

			a(6) = 25 because the digits in the 5th row of Pascal's triangle are 1,5,(1,0),(1,0),5,1, the product of the nonzero terms is 25. - _Richard M. Green_, Feb 12 2014

Cf. A007318, A066600, A086993, A051801.

A086992[n_]:= Times @@ DeleteCases[0]@Flatten@IntegerDigits@Table[Binomial[n, k], {k, 0, n}] (* JungHwan Min, Dec 07 2015 *)

A051801(n)=my(v=select(k->k>1, digits(n))); prod(i=1, #v, v[i])
a(n)=prod(k=1,(n-1)\2,A051801(binomial(n,k)))^2*if(n%2,1,A051801(binomial(n,n/2))) \\ Charles R Greathouse IV, Dec 08 2015

cp's OEIS Frontend

A089520 In Conway's Game of Life, the number of steps it takes for an n X n square, in which all the cells are in the "on" state, to die out or start to cycle, or -1 if there is no cycle.

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A086973 Period of oscillator reached starting with a segment of n consecutive live cells and applying the LongLife 2D rule (see comment).

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PARI

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A086992 Product of nonzero digits in n-th row of Pascal's triangle.

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