A136279 Number of n X n Life configurations that are "flip-flops" (Life cycles of period 2).

0, 0, 1, 12, 43, 163, 8424, 582769, 40292074

Offset

1,4

Comments

These counts have not been reduced to take account of the symmetries of the board.

References

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982; see Chapter 25.

D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.

Links

Table of n, a(n) for n=1..9.

Example

The 12 solutions for n=4 belong to four isomorphism classes under symmetry:
The blinker, four cases:
..State 1. ..State 2.
.......... ....*.....
...***.... ....*.....
.......... ....*.....
.......... ..........
The toad, four cases:
..State 1. ..State 2.
.....*.... ..........
...*..*... ....***...
...*..*... ...***....
....*..... ..........
The beacon, two cases:
..State 1. ..State 2.
.....**... .....**...
......*... .....**...
...*...... ...**.....
...**..... ...**.....
The clock, two cases:
..State 1. ..State 2.
.....*.... ....*.....
...*.*.... .....**...
....*.*... ...**.....
....*..... .....*....

Crossrefs

Cf. A134963, A136278, A136280.

Sequence in context: A062749 A251929 A004636 * A012471 A116187 A009790

Adjacent sequences: A136276 A136277 A136278 * A136280 A136281 A136282

Keyword

nonn

Author

Don Knuth, Mar 26 2008

Status

approved