A056098 Minimum value in the distribution by first value of Prufer code of noncrossing spanning trees on a circle of n+2 points.

1, 2, 5, 17, 68, 267, 1230, 5564, 27575, 136644, 714772, 3743265, 20353789, 110723361, 619347223, 3464770044, 19801412122, 113178582936

Offset: 3

Author

David S. Hough (hough(AT)gwu.edu), Aug 04 2000

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A056096.