A129181 - cp's OEIS frontend

A129181 Triangle read by rows: T(n,k) is the number of Motzkin paths of length n such that the area between the x-axis and the path is k (n>=0; 0<=k<=floor(n^2/4)).

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	3
9	3
10	1
11	1
12	1
13	4
14	6
15	4
16	3
17	2
18	1
19	1
20	5
21	10
22	10
23	8
24	7
25	5
26	3
27	1
28	1
29	1
30	6
31	15
32	20
33	19
34	18
35	16
36	12
37	8
38	6
39	3
40	2
41	1
42	1
43	7
44	21
45	35
46	40
47	41
48	41
49	36
50	29
51	23
52	18
53	12
54	9
55	5
56	3
57	1
58	1
59	1
60	8
61	28
62	56
63	76
64	86
65	93
66	92
67	83
68	72
69	62
70	50
71	40
72	30
73	22
74	14
75	10
76	6
77	3
78	2
79	1
80	1
81	9
82	36
83	84
84	133
85	168

[1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 1, 4, 6, 4, 3, 2, 1, 1, 5, 10, 10, 8, 7, 5, 3, 1, 1, 1, 6, 15, 20, 19, 18, 16, 12, 8, 6, 3, 2, 1, 1, 7, 21, 35, 40, 41, 41, 36, 29, 23, 18, 12, 9, 5, 3, 1, 1, 1, 8, 28, 56, 76, 86, 93, 92, 83, 72, 62, 50, 40, 30, 22, 14, 10, 6, 3, 2, 1, 1, 9, 36, 84, 133, 168]

cp's OEIS Frontend

A129181 Triangle read by rows: T(n,k) is the number of Motzkin paths of length n such that the area between the x-axis and the path is k (n>=0; 0<=k<=floor(n^2/4)).

Table of values

List of values

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	3
9	3
10	1
11	1
12	1
13	4
14	6
15	4
16	3
17	2
18	1
19	1
20	5
21	10
22	10
23	8
24	7
25	5
26	3
27	1
28	1
29	1
30	6
31	15
32	20
33	19
34	18
35	16
36	12
37	8
38	6
39	3
40	2
41	1
42	1
43	7
44	21
45	35
46	40
47	41
48	41
49	36
50	29
51	23
52	18
53	12
54	9
55	5
56	3
57	1
58	1
59	1
60	8
61	28
62	56
63	76
64	86
65	93
66	92
67	83
68	72
69	62
70	50
71	40
72	30
73	22
74	14
75	10
76	6
77	3
78	2
79	1
80	1
81	9
82	36
83	84
84	133
85	168

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	3
9	3
10	1
11	1
12	1
13	4
14	6
15	4
16	3
17	2
18	1
19	1
20	5
21	10
22	10
23	8
24	7
25	5
26	3
27	1
28	1
29	1
30	6
31	15
32	20
33	19
34	18
35	16
36	12
37	8
38	6
39	3
40	2
41	1
42	1
43	7
44	21
45	35
46	40
47	41
48	41
49	36
50	29
51	23
52	18
53	12
54	9
55	5
56	3
57	1
58	1
59	1
60	8
61	28
62	56
63	76
64	86
65	93
66	92
67	83
68	72
69	62
70	50
71	40
72	30
73	22
74	14
75	10
76	6
77	3
78	2
79	1
80	1
81	9
82	36
83	84
84	133
85	168

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	3
9	3
10	1
11	1
12	1
13	4
14	6
15	4
16	3
17	2
18	1
19	1
20	5
21	10
22	10
23	8
24	7
25	5
26	3
27	1
28	1
29	1
30	6
31	15
32	20
33	19
34	18
35	16
36	12
37	8
38	6
39	3
40	2
41	1
42	1
43	7
44	21
45	35
46	40
47	41
48	41
49	36
50	29
51	23
52	18
53	12
54	9
55	5
56	3
57	1
58	1
59	1
60	8
61	28
62	56
63	76
64	86
65	93
66	92
67	83
68	72
69	62
70	50
71	40
72	30
73	22
74	14
75	10
76	6
77	3
78	2
79	1
80	1
81	9
82	36
83	84
84	133
85	168