## Happy Pentominos |
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## The F Pentomino Is A Methuselah

In John Conway's Game of Life, the F pentomino has a secure reputation as a methuselah. If you don't know about Conway's Game of Life, it is well worth investigating. Many sites provide Java applets. In particular, Alan Hensel. There you can open RPENTO.LIF and play it. The GoL people keep on calling it the R pentomino... what dotheyknow!## Counting Poly-ominoes

There is one domino and 12 pentominoes. In trying to count the N-ominoes, nobody has been able to go much beyond the 24-ominoes. This series of numbers is a documentedInteger Series. To quote from another site :And... connections, connections, Neil Sloane and I work in the same building, recently named Shannon Lab! And here is a link linking Golomb, Sloane and Shannon!The number ofncell polyominoes (that allow holes) forn= 1,2,...,15, is 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238951, 901971, 3426576.This is sequence

A000105(M1425) in Sloane's database of integer sequences.The number of

ncell polyominoes (without holes) forn= 1,2,...,15, is 1, 1, 2, 5, 12, 35, 107, 363, 1248, 4460, 16094, 58937, 217117, 805475, 3001211. This is sequenceA000104(M1424) in Sloane's database of integer sequences.

The program used is due to John Boyer, and is based on a paper of Redelmeier (Discrete Math. 36 (1981) 191-203).## Lattice Animals

In 2D percolation theory, N-ominoes are refered to as lattice animals. Now that is cute! This link also refers to work not only by some of the above suspects, J. Conway and S. W. Golomb, but also by R. L. Rivest of MIT, the R in the famous RSA encryption algorithm. These are only the most famous names, of course. The point is, if they can spend a few hours with pentominoes, so can you! (and me!)Now, from percolation theory to java... hmm, I don't smell a real connection there!