A138159 - cp's OEIS frontend

A138159 Triangle read by rows: T(n,k) is the number of permutations of [n] having k occurrences of the pattern 321 (n>=1, 0<=k<=n(n-1)(n-2)/6).

n	a(n)
0	1
1	1
2	2
3	5
4	1
5	14
6	6
7	3
8	0
9	1
10	42
11	27
12	24
13	7
14	9
15	6
16	0
17	4
18	0
19	0
20	1
21	132
22	110
23	133
24	70
25	74
26	54
27	37
28	32
29	24
30	12
31	16
32	6
33	6
34	8
35	0
36	0
37	5
38	0
39	0
40	0
41	1
42	429
43	429
44	635
45	461
46	507
47	395
48	387
49	320
50	260
51	232
52	191
53	162
54	104
55	130
56	100
57	24
58	74
59	62
60	18
61	32
62	10
63	30
64	13
65	8
66	0
67	10
68	10
69	0
70	0
71	0
72	6
73	0
74	0
75	0
76	0
77	1

[1, 1, 2, 5, 1, 14, 6, 3, 0, 1, 42, 27, 24, 7, 9, 6, 0, 4, 0, 0, 1, 132, 110, 133, 70, 74, 54, 37, 32, 24, 12, 16, 6, 6, 8, 0, 0, 5, 0, 0, 0, 1, 429, 429, 635, 461, 507, 395, 387, 320, 260, 232, 191, 162, 104, 130, 100, 24, 74, 62, 18, 32, 10, 30, 13, 8, 0, 10, 10, 0, 0, 0, 6, 0, 0, 0, 0, 1]

cp's OEIS Frontend

A138159 Triangle read by rows: T(n,k) is the number of permutations of [n] having k occurrences of the pattern 321 (n>=1, 0<=k<=n(n-1)(n-2)/6).

Table of values

List of values

n	a(n)
0	1
1	1
2	2
3	5
4	1
5	14
6	6
7	3
8	0
9	1
10	42
11	27
12	24
13	7
14	9
15	6
16	0
17	4
18	0
19	0
20	1
21	132
22	110
23	133
24	70
25	74
26	54
27	37
28	32
29	24
30	12
31	16
32	6
33	6
34	8
35	0
36	0
37	5
38	0
39	0
40	0
41	1
42	429
43	429
44	635
45	461
46	507
47	395
48	387
49	320
50	260
51	232
52	191
53	162
54	104
55	130
56	100
57	24
58	74
59	62
60	18
61	32
62	10
63	30
64	13
65	8
66	0
67	10
68	10
69	0
70	0
71	0
72	6
73	0
74	0
75	0
76	0
77	1

n	a(n)
0	1
1	1
2	2
3	5
4	1
5	14
6	6
7	3
8	0
9	1
10	42
11	27
12	24
13	7
14	9
15	6
16	0
17	4
18	0
19	0
20	1
21	132
22	110
23	133
24	70
25	74
26	54
27	37
28	32
29	24
30	12
31	16
32	6
33	6
34	8
35	0
36	0
37	5
38	0
39	0
40	0
41	1
42	429
43	429
44	635
45	461
46	507
47	395
48	387
49	320
50	260
51	232
52	191
53	162
54	104
55	130
56	100
57	24
58	74
59	62
60	18
61	32
62	10
63	30
64	13
65	8
66	0
67	10
68	10
69	0
70	0
71	0
72	6
73	0
74	0
75	0
76	0
77	1

n	a(n)
0	1
1	1
2	2
3	5
4	1
5	14
6	6
7	3
8	0
9	1
10	42
11	27
12	24
13	7
14	9
15	6
16	0
17	4
18	0
19	0
20	1
21	132
22	110
23	133
24	70
25	74
26	54
27	37
28	32
29	24
30	12
31	16
32	6
33	6
34	8
35	0
36	0
37	5
38	0
39	0
40	0
41	1
42	429
43	429
44	635
45	461
46	507
47	395
48	387
49	320
50	260
51	232
52	191
53	162
54	104
55	130
56	100
57	24
58	74
59	62
60	18
61	32
62	10
63	30
64	13
65	8
66	0
67	10
68	10
69	0
70	0
71	0
72	6
73	0
74	0
75	0
76	0
77	1