A300322 - cp's OEIS frontend

A300322 Number T(n,k) of Dyck paths of semilength n such that 2k is the difference between the area under the right half of the path and the area under the left half of the path; triangle T(n,k), n>=0, -floor(n(n-1)/6) <= k <= floor(n*(n-1)/6), read by rows.

n	a(n)
0	1
1	1
2	2
3	1
4	3
5	1
6	1
7	3
8	6
9	3
10	1
11	2
12	5
13	8
14	12
15	8
16	5
17	2
18	1
19	4
20	9
21	16
22	22
23	28
24	22
25	16
26	9
27	4
28	1
29	1
30	4
31	11
32	21
33	34
34	49
35	60
36	69
37	60
38	49
39	34
40	21
41	11
42	4
43	1
44	2
45	7
46	15
47	31
48	53
49	82
50	114
51	147
52	171
53	186
54	171
55	147
56	114
57	82
58	53
59	31
60	15
61	7
62	2
63	1
64	5
65	13
66	30
67	56
68	95
69	150
70	216
71	293
72	371
73	445
74	495
75	522
76	495
77	445
78	371
79	293
80	216
81	150
82	95
83	56
84	30
85	13
86	5
87	1

[1, 1, 2, 1, 3, 1, 1, 3, 6, 3, 1, 2, 5, 8, 12, 8, 5, 2, 1, 4, 9, 16, 22, 28, 22, 16, 9, 4, 1, 1, 4, 11, 21, 34, 49, 60, 69, 60, 49, 34, 21, 11, 4, 1, 2, 7, 15, 31, 53, 82, 114, 147, 171, 186, 171, 147, 114, 82, 53, 31, 15, 7, 2, 1, 5, 13, 30, 56, 95, 150, 216, 293, 371, 445, 495, 522, 495, 445, 371, 293, 216, 150, 95, 56, 30, 13, 5, 1]

cp's OEIS Frontend

A300322 Number T(n,k) of Dyck paths of semilength n such that 2k is the difference between the area under the right half of the path and the area under the left half of the path; triangle T(n,k), n>=0, -floor(n(n-1)/6) <= k <= floor(n*(n-1)/6), read by rows.

Table of values

List of values

n	a(n)
0	1
1	1
2	2
3	1
4	3
5	1
6	1
7	3
8	6
9	3
10	1
11	2
12	5
13	8
14	12
15	8
16	5
17	2
18	1
19	4
20	9
21	16
22	22
23	28
24	22
25	16
26	9
27	4
28	1
29	1
30	4
31	11
32	21
33	34
34	49
35	60
36	69
37	60
38	49
39	34
40	21
41	11
42	4
43	1
44	2
45	7
46	15
47	31
48	53
49	82
50	114
51	147
52	171
53	186
54	171
55	147
56	114
57	82
58	53
59	31
60	15
61	7
62	2
63	1
64	5
65	13
66	30
67	56
68	95
69	150
70	216
71	293
72	371
73	445
74	495
75	522
76	495
77	445
78	371
79	293
80	216
81	150
82	95
83	56
84	30
85	13
86	5
87	1

n	a(n)
0	1
1	1
2	2
3	1
4	3
5	1
6	1
7	3
8	6
9	3
10	1
11	2
12	5
13	8
14	12
15	8
16	5
17	2
18	1
19	4
20	9
21	16
22	22
23	28
24	22
25	16
26	9
27	4
28	1
29	1
30	4
31	11
32	21
33	34
34	49
35	60
36	69
37	60
38	49
39	34
40	21
41	11
42	4
43	1
44	2
45	7
46	15
47	31
48	53
49	82
50	114
51	147
52	171
53	186
54	171
55	147
56	114
57	82
58	53
59	31
60	15
61	7
62	2
63	1
64	5
65	13
66	30
67	56
68	95
69	150
70	216
71	293
72	371
73	445
74	495
75	522
76	495
77	445
78	371
79	293
80	216
81	150
82	95
83	56
84	30
85	13
86	5
87	1

cp's OEIS Frontend

A300322 Number T(n,k) of Dyck paths of semilength n such that 2*k is the difference between the area under the right half of the path and the area under the left half of the path; triangle T(n,k), n>=0, -floor(n*(n-1)/6) <= k <= floor(n*(n-1)/6), read by rows.

Table of values

List of values

A300322 Number T(n,k) of Dyck paths of semilength n such that 2k is the difference between the area under the right half of the path and the area under the left half of the path; triangle T(n,k), n>=0, -floor(n(n-1)/6) <= k <= floor(n*(n-1)/6), read by rows.

n	a(n)
0	1
1	1
2	2
3	1
4	3
5	1
6	1
7	3
8	6
9	3
10	1
11	2
12	5
13	8
14	12
15	8
16	5
17	2
18	1
19	4
20	9
21	16
22	22
23	28
24	22
25	16
26	9
27	4
28	1
29	1
30	4
31	11
32	21
33	34
34	49
35	60
36	69
37	60
38	49
39	34
40	21
41	11
42	4
43	1
44	2
45	7
46	15
47	31
48	53
49	82
50	114
51	147
52	171
53	186
54	171
55	147
56	114
57	82
58	53
59	31
60	15
61	7
62	2
63	1
64	5
65	13
66	30
67	56
68	95
69	150
70	216
71	293
72	371
73	445
74	495
75	522
76	495
77	445
78	371
79	293
80	216
81	150
82	95
83	56
84	30
85	13
86	5
87	1