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COMMENT
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Total in distribution is # t_n of ternary trees and one can prove first and last values in each distribution is t_{n-1}. Maximum appears to occur at 2, minimum near end; perhaps monotone between first, max, min, last. Distributions of Prufer code initial values, starting with 3 points: [1,1,1], [3,4,2,3], [12,17,9,5,12], [55,80,44,22,17,55], [273,403,227,112,68,72,273], [1428,2128,1218,613,335,267,345,1428].
First 200 values (n=3 to 202) of min occur at k=floor((n+5)/2); first 200 values of max (series A056096) occur at k=2.
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EXAMPLE
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There are 12 noncrossing spanning trees on a circle of 4 points. The first values of their Prufer codes have distribution [3,4,2,3], e.g. 3 start with 1, 4 with 2, 2 with 3 and 3 with 4. The minimum value is a(4) = 2.
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