A129179 - cp's OEIS frontend

A129179 Triangle read by rows: T(n, k) is the number of Schroeder paths of semilength n such that the area between the x-axis and the path is k (n >= 0; 0 <= k <= n^2).

n	a(n)
0	1
1	1
2	1
3	1
4	2
5	1
6	1
7	1
8	1
9	3
10	3
11	3
12	4
13	3
14	2
15	1
16	1
17	1
18	1
19	4
20	6
21	7
22	10
23	11
24	10
25	9
26	8
27	7
28	5
29	4
30	3
31	2
32	1
33	1
34	1
35	1
36	5
37	10
38	14
39	21
40	28
41	31
42	33
43	34
44	34
45	31
46	27
47	25
48	22
49	17
50	14
51	13
52	10
53	7
54	5
55	4
56	3
57	2
58	1
59	1
60	1
61	1
62	6
63	15
64	25
65	40
66	60
67	77
68	92
69	106
70	117
71	122
72	121
73	120
74	116
75	107
76	98
77	91
78	82
79	71
80	62
81	54
82	45

[1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 3, 4, 3, 2, 1, 1, 1, 1, 4, 6, 7, 10, 11, 10, 9, 8, 7, 5, 4, 3, 2, 1, 1, 1, 1, 5, 10, 14, 21, 28, 31, 33, 34, 34, 31, 27, 25, 22, 17, 14, 13, 10, 7, 5, 4, 3, 2, 1, 1, 1, 1, 6, 15, 25, 40, 60, 77, 92, 106, 117, 122, 121, 120, 116, 107, 98, 91, 82, 71, 62, 54, 45]

cp's OEIS Frontend

A129179 Triangle read by rows: T(n, k) is the number of Schroeder paths of semilength n such that the area between the x-axis and the path is k (n >= 0; 0 <= k <= n^2).

Table of values

List of values

n	a(n)
0	1
1	1
2	1
3	1
4	2
5	1
6	1
7	1
8	1
9	3
10	3
11	3
12	4
13	3
14	2
15	1
16	1
17	1
18	1
19	4
20	6
21	7
22	10
23	11
24	10
25	9
26	8
27	7
28	5
29	4
30	3
31	2
32	1
33	1
34	1
35	1
36	5
37	10
38	14
39	21
40	28
41	31
42	33
43	34
44	34
45	31
46	27
47	25
48	22
49	17
50	14
51	13
52	10
53	7
54	5
55	4
56	3
57	2
58	1
59	1
60	1
61	1
62	6
63	15
64	25
65	40
66	60
67	77
68	92
69	106
70	117
71	122
72	121
73	120
74	116
75	107
76	98
77	91
78	82
79	71
80	62
81	54
82	45

n	a(n)
0	1
1	1
2	1
3	1
4	2
5	1
6	1
7	1
8	1
9	3
10	3
11	3
12	4
13	3
14	2
15	1
16	1
17	1
18	1
19	4
20	6
21	7
22	10
23	11
24	10
25	9
26	8
27	7
28	5
29	4
30	3
31	2
32	1
33	1
34	1
35	1
36	5
37	10
38	14
39	21
40	28
41	31
42	33
43	34
44	34
45	31
46	27
47	25
48	22
49	17
50	14
51	13
52	10
53	7
54	5
55	4
56	3
57	2
58	1
59	1
60	1
61	1
62	6
63	15
64	25
65	40
66	60
67	77
68	92
69	106
70	117
71	122
72	121
73	120
74	116
75	107
76	98
77	91
78	82
79	71
80	62
81	54
82	45

n	a(n)
0	1
1	1
2	1
3	1
4	2
5	1
6	1
7	1
8	1
9	3
10	3
11	3
12	4
13	3
14	2
15	1
16	1
17	1
18	1
19	4
20	6
21	7
22	10
23	11
24	10
25	9
26	8
27	7
28	5
29	4
30	3
31	2
32	1
33	1
34	1
35	1
36	5
37	10
38	14
39	21
40	28
41	31
42	33
43	34
44	34
45	31
46	27
47	25
48	22
49	17
50	14
51	13
52	10
53	7
54	5
55	4
56	3
57	2
58	1
59	1
60	1
61	1
62	6
63	15
64	25
65	40
66	60
67	77
68	92
69	106
70	117
71	122
72	121
73	120
74	116
75	107
76	98
77	91
78	82
79	71
80	62
81	54
82	45