General Trees

How many unlabeled trees exist on $n$ vertices is well studied, and some of this sequence is presented in Table 1, in which we also present how long² it took us to generate all the trees of order $n$. In the table, $G_w(n)$ and $G_s(n)$ denote the wall clock and system time used in generating all the trees of order $n$. $L_w(n)$ and $L_s(n)$ are subscripted similarly, and denote time to gracefully label all tree of order $n$. $T(n)$ is simply how many trees of order $n$ exist.

Table 1: Unlabeled trees of order $n$, and time for their generation. $L_w(15)$ and $L_s(15)$ require at least 24 hours.

$n$	$G_w(n)$	$G_s(n)$	$L_w(n)$	$L_s(n)$	$T(n)$
1	4.2e-5s	0.0s	5.8e-5s	0.0s	1
2	2.0e-5s	0.0s	9.4e-5s	0.0s	1
3	.028s	0.0s	1.0e-4s	0.0s	1
4	.038s	0.002s	2.99e-4s	0.0s	2
5	.123s	0.006s	6.27e-4s	0.001s	3
6	.196s	0.014s	0.002s	0.002s	6
7	.488s	0.035s	0.018s	0.013s	11
8	1.065s	0.098s	0.057s	0.057s	23
9	2.627s	0.318s	0.474s	0.443s	47
10	6.574s	1.198s	2.818s	2.449s	106
11	19.546s	6.005s	34.358	29.116s	235
12	1m6s	32.905s	2m31s	2m6s	551
13	4m54s	3m11s	44m6s	39m46s	1301
14	31m53s	21m51s	7h0m6s	6h14m35s	3159
15	3h49m11s	2h30m39s	?	?	7741
16	?	?	?	?	19320
17	?	?	?	?	48629
18	?	?	?	?	123867