A367764 a(n) is the numerator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears in the Eden growth model on the square lattice (see A367760), when n square cells have been added.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 7, 7, 1, 1, 1, 23, 49, 1, 1, 53, 1, 107, 1, 49, 1, 107, 1, 23, 1, 1, 1, 1, 137, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 7, 1, 2797, 70037, 70037, 31, 31, 2797, 3517, 1, 41, 653, 49541, 1, 3517, 71, 67, 41, 899, 2797, 653, 1, 1, 1, 1, 653, 1, 1

Offset

1,14

Comments

Apparently, the probabilities a(n)/A367765(n) are given in Eden (1958) for polyominoes up to 8 cells.

Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.

References

Murray Eden, A probabilistic model for morphogenesis, in: Symposium on Information Theory in Biology (Gatlinburg 1956), pp. 359-370, Pergamon Press, New York, 1958.

Links

Table of n, a(n) for n=1..82.

Murray Eden, A two-dimensional growth process, in: 4th Berkeley Symposium on Mathematical Statistics and Probability (Berkeley 1960), vol. 4, pp. 223-239, University of California Press, Berkeley, 1961.

Index entries for sequences related to polyominoes.

Formula

a(n)/A367765(n) = (A367760(n)/A367761(n))/A335573(n+1).

Example

As an irregular triangle:
  1;
  1;
  1, 1;
  1, 1, 1, 1, 1;
  1, 1, 1, 1, 7, 1, 1, 7, 7, 1, 1, 1;
  ...

Crossrefs

Cf. A000105, A246521, A335573, A367675, A367760, A367761, A367765 (denominators), A367766.

Sequence in context: A105395 A120437 A336459 * A174095 A305607 A229779

Adjacent sequences: A367761 A367762 A367763 * A367765 A367766 A367767

Keyword

nonn,frac,tabf

Author

Pontus von Brömssen, Dec 02 2023

Status

approved