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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. 2
1, 4, 17, 80, 403, 2128, 11628, 65208, 373175, 2170740, 12797265, 76292736, 459162452, 2786017120, 17024247304, 104673837384, 647113502847, 4020062732140 (list; graph; refs; listen; history; text; internal format)
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 A245377 A204326

Adjacent sequences:  A056093 A056094 A056095 * A056097 A056098 A056099

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified January 17 10:57 EST 2019. Contains 319218 sequences. (Running on oeis4.)