A221857 - cp's OEIS frontend

A221857 Number A(n,k) of shapes of balanced k-ary trees with n nodes, where a tree is balanced if the total number of nodes in subtrees corresponding to the branches of any node differ by at most one; square array A(n,k), n>=0, k>=0, read by antidiagonals.

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	0
6	1
7	1
8	1
9	0
10	1
11	1
12	2
13	1
14	0
15	1
16	1
17	3
18	1
19	1
20	0
21	1
22	1
23	4
24	3
25	4
26	1
27	0
28	1
29	1
30	5
31	6
32	1
33	4
34	1
35	0
36	1
37	1
38	6
39	10
40	4
41	9
42	4
43	1
44	0
45	1
46	1
47	7
48	15
49	10
50	1
51	27
52	1
53	1
54	0
55	1
56	1
57	8
58	21
59	20
60	5
61	16
62	27
63	8
64	1
65	0
66	1
67	1
68	9
69	28
70	35
71	15
72	1
73	96
74	81
75	16
76	1
77	0
78	1
79	1
80	10
81	36
82	56
83	35
84	6
85	25
86	256
87	81
88	32
89	1
90	0

[1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 3, 1, 1, 0, 1, 1, 4, 3, 4, 1, 0, 1, 1, 5, 6, 1, 4, 1, 0, 1, 1, 6, 10, 4, 9, 4, 1, 0, 1, 1, 7, 15, 10, 1, 27, 1, 1, 0, 1, 1, 8, 21, 20, 5, 16, 27, 8, 1, 0, 1, 1, 9, 28, 35, 15, 1, 96, 81, 16, 1, 0, 1, 1, 10, 36, 56, 35, 6, 25, 256, 81, 32, 1, 0]

cp's OEIS Frontend

A221857 Number A(n,k) of shapes of balanced k-ary trees with n nodes, where a tree is balanced if the total number of nodes in subtrees corresponding to the branches of any node differ by at most one; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Table of values

List of values

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	0
6	1
7	1
8	1
9	0
10	1
11	1
12	2
13	1
14	0
15	1
16	1
17	3
18	1
19	1
20	0
21	1
22	1
23	4
24	3
25	4
26	1
27	0
28	1
29	1
30	5
31	6
32	1
33	4
34	1
35	0
36	1
37	1
38	6
39	10
40	4
41	9
42	4
43	1
44	0
45	1
46	1
47	7
48	15
49	10
50	1
51	27
52	1
53	1
54	0
55	1
56	1
57	8
58	21
59	20
60	5
61	16
62	27
63	8
64	1
65	0
66	1
67	1
68	9
69	28
70	35
71	15
72	1
73	96
74	81
75	16
76	1
77	0
78	1
79	1
80	10
81	36
82	56
83	35
84	6
85	25
86	256
87	81
88	32
89	1
90	0

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	0
6	1
7	1
8	1
9	0
10	1
11	1
12	2
13	1
14	0
15	1
16	1
17	3
18	1
19	1
20	0
21	1
22	1
23	4
24	3
25	4
26	1
27	0
28	1
29	1
30	5
31	6
32	1
33	4
34	1
35	0
36	1
37	1
38	6
39	10
40	4
41	9
42	4
43	1
44	0
45	1
46	1
47	7
48	15
49	10
50	1
51	27
52	1
53	1
54	0
55	1
56	1
57	8
58	21
59	20
60	5
61	16
62	27
63	8
64	1
65	0
66	1
67	1
68	9
69	28
70	35
71	15
72	1
73	96
74	81
75	16
76	1
77	0
78	1
79	1
80	10
81	36
82	56
83	35
84	6
85	25
86	256
87	81
88	32
89	1
90	0

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	0
6	1
7	1
8	1
9	0
10	1
11	1
12	2
13	1
14	0
15	1
16	1
17	3
18	1
19	1
20	0
21	1
22	1
23	4
24	3
25	4
26	1
27	0
28	1
29	1
30	5
31	6
32	1
33	4
34	1
35	0
36	1
37	1
38	6
39	10
40	4
41	9
42	4
43	1
44	0
45	1
46	1
47	7
48	15
49	10
50	1
51	27
52	1
53	1
54	0
55	1
56	1
57	8
58	21
59	20
60	5
61	16
62	27
63	8
64	1
65	0
66	1
67	1
68	9
69	28
70	35
71	15
72	1
73	96
74	81
75	16
76	1
77	0
78	1
79	1
80	10
81	36
82	56
83	35
84	6
85	25
86	256
87	81
88	32
89	1
90	0