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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.
8
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
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.
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
KEYWORD
nonn,frac,tabf
AUTHOR
STATUS
approved