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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.

%I A367764 #7 Dec 03 2023 09:11:48
%S A367764 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,
%T A367764 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,
%U A367764 70037,31,31,2797,3517,1,41,653,49541,1,3517,71,67,41,899,2797,653,1,1,1,1,653,1,1
%N 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.
%C A367764 Apparently, the probabilities a(n)/A367765(n) are given in Eden (1958) for polyominoes up to 8 cells.
%C A367764 Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.
%D A367764 Murray Eden, A probabilistic model for morphogenesis, in: Symposium on Information Theory in Biology (Gatlinburg 1956), pp. 359-370, Pergamon Press, New York, 1958.
%H A367764 Murray Eden, <a href="https://projecteuclid.org/ebooks/berkeley-symposium-on-mathematical-statistics-and-probability/Proceedings-of-the-Fourth-Berkeley-Symposium-on-Mathematical-Statistics-and/chapter/A-Two-dimensional-Growth-Process/bsmsp/1200512888">A two-dimensional growth process</a>, in: 4th Berkeley Symposium on Mathematical Statistics and Probability (Berkeley 1960), vol. 4, pp. 223-239, University of California Press, Berkeley, 1961.
%H A367764 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.
%F A367764 a(n)/A367765(n) = (A367760(n)/A367761(n))/A335573(n+1).
%e A367764 As an irregular triangle:
%e A367764   1;
%e A367764   1;
%e A367764   1, 1;
%e A367764   1, 1, 1, 1, 1;
%e A367764   1, 1, 1, 1, 7, 1, 1, 7, 7, 1, 1, 1;
%e A367764   ...
%Y A367764 Cf. A000105, A246521, A335573, A367675, A367760, A367761, A367765 (denominators), A367766.
%K A367764 nonn,frac,tabf
%O A367764 1,14
%A A367764 _Pontus von Brömssen_, Dec 02 2023