A143364 - cp's OEIS frontend

A143364 Triangle read by rows: T(n,k) is the number of {0-1-2}-trees with n edges and k protected vertices (0<=k<=n-1). A {0-1-2}-tree is an ordered tree in which the outdegree of every vertex is 0, 1, or 2. A protected vertex in an ordered tree is a vertex at least 2 edges away from its leaf descendants.

n	a(n)
1	1
2	1
3	1
4	2
5	1
6	1
7	2
8	5
9	1
10	1
11	4
12	6
13	9
14	1
15	1
16	4
17	19
18	12
19	14
20	1
21	1
22	8
23	24
24	53
25	20
26	20
27	1
28	1
29	8
30	62
31	78
32	116
33	30
34	27
35	1
36	1
37	16
38	80
39	250
40	190
41	220
42	42
43	35
44	1
45	1
46	16
47	184
48	382
49	735
50	390
51	379
52	56
53	44
54	1
55	1
56	32
57	240
58	1020
59	1270
60	1785
61	714
62	609
63	72
64	54
65	1
66	1
67	32
68	512
69	1580
70	3900
71	3390
72	3808

[1, 1, 1, 2, 1, 1, 2, 5, 1, 1, 4, 6, 9, 1, 1, 4, 19, 12, 14, 1, 1, 8, 24, 53, 20, 20, 1, 1, 8, 62, 78, 116, 30, 27, 1, 1, 16, 80, 250, 190, 220, 42, 35, 1, 1, 16, 184, 382, 735, 390, 379, 56, 44, 1, 1, 32, 240, 1020, 1270, 1785, 714, 609, 72, 54, 1, 1, 32, 512, 1580, 3900, 3390, 3808]

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