A056096 Maximum value in the distribution by first value of Prufer code of noncrossing spanning trees on a circle of n+2 points; perhaps the number whose Prufer code starts with 2.

1, 4, 17, 80, 403, 2128, 11628, 65208, 373175, 2170740, 12797265, 76292736, 459162452, 2786017120, 17024247304, 104673837384, 647113502847, 4020062732140

Offset

3,2

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],[1428,2128,1218,603,335,267,345,1428].

First 200 values (n=3 to 202) of max occur at k=2; first 200 values of min (series A056098) occur at k=floor((n+5)/2).

Links

Table of n, a(n) for n=3..20.

Formula

G.f.: seems to be (g+1)/(1-g)^3 where g*(1-g)^2 = x. - Mark van Hoeij, Nov 10 2011

Example

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 and so on. The maximum is a(4) = 4.

Crossrefs

Cf. A056098.

Sequence in context: A110307 A206228 A089165 * A257084 A371915 A245377

Adjacent sequences: A056093 A056094 A056095 * A056097 A056098 A056099

Keyword

nonn,more

Author

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

Status

approved