A247749 - cp's OEIS frontend

A247749 Number T(n,k) of lattice paths from (0,0) to (n,0) that do not go below the x-axis or above the diagonal x=y, consist of steps u=(1,1), U=(1,3), H=(1,0), d=(1,-1) and D=(1,-3) for which the area below the path is k; triangle T(n,k), n>=0, read by rows.

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	3
9	3
10	2
11	2
12	0
13	1
14	1
15	4
16	6
17	6
18	6
19	3
20	4
21	2
22	1
23	1
24	1
25	5
26	10
27	13
28	15
29	12
30	14
31	15
32	9
33	12
34	5
35	5
36	1
37	1
38	1
39	6
40	15
41	24
42	32
43	33
44	37
45	46
46	40
47	43
48	34
49	28
50	23
51	16
52	10
53	5
54	2
55	1
56	1
57	7
58	21
59	40
60	61
61	75
62	88
63	114
64	122
65	134
66	137
67	118
68	127
69	101
70	99
71	69
72	68
73	41
74	38
75	19
76	17
77	5
78	5
79	0
80	1

[1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 2, 2, 0, 1, 1, 4, 6, 6, 6, 3, 4, 2, 1, 1, 1, 5, 10, 13, 15, 12, 14, 15, 9, 12, 5, 5, 1, 1, 1, 6, 15, 24, 32, 33, 37, 46, 40, 43, 34, 28, 23, 16, 10, 5, 2, 1, 1, 7, 21, 40, 61, 75, 88, 114, 122, 134, 137, 118, 127, 101, 99, 69, 68, 41, 38, 19, 17, 5, 5, 0, 1]

cp's OEIS Frontend

A247749 Number T(n,k) of lattice paths from (0,0) to (n,0) that do not go below the x-axis or above the diagonal x=y, consist of steps u=(1,1), U=(1,3), H=(1,0), d=(1,-1) and D=(1,-3) for which the area below the path is k; triangle T(n,k), n>=0, read by rows.

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	2
11	2
12	0
13	1
14	1
15	4
16	6
17	6
18	6
19	3
20	4
21	2
22	1
23	1
24	1
25	5
26	10
27	13
28	15
29	12
30	14
31	15
32	9
33	12
34	5
35	5
36	1
37	1
38	1
39	6
40	15
41	24
42	32
43	33
44	37
45	46
46	40
47	43
48	34
49	28
50	23
51	16
52	10
53	5
54	2
55	1
56	1
57	7
58	21
59	40
60	61
61	75
62	88
63	114
64	122
65	134
66	137
67	118
68	127
69	101
70	99
71	69
72	68
73	41
74	38
75	19
76	17
77	5
78	5
79	0
80	1

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	3
9	3
10	2
11	2
12	0
13	1
14	1
15	4
16	6
17	6
18	6
19	3
20	4
21	2
22	1
23	1
24	1
25	5
26	10
27	13
28	15
29	12
30	14
31	15
32	9
33	12
34	5
35	5
36	1
37	1
38	1
39	6
40	15
41	24
42	32
43	33
44	37
45	46
46	40
47	43
48	34
49	28
50	23
51	16
52	10
53	5
54	2
55	1
56	1
57	7
58	21
59	40
60	61
61	75
62	88
63	114
64	122
65	134
66	137
67	118
68	127
69	101
70	99
71	69
72	68
73	41
74	38
75	19
76	17
77	5
78	5
79	0
80	1

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	3
9	3
10	2
11	2
12	0
13	1
14	1
15	4
16	6
17	6
18	6
19	3
20	4
21	2
22	1
23	1
24	1
25	5
26	10
27	13
28	15
29	12
30	14
31	15
32	9
33	12
34	5
35	5
36	1
37	1
38	1
39	6
40	15
41	24
42	32
43	33
44	37
45	46
46	40
47	43
48	34
49	28
50	23
51	16
52	10
53	5
54	2
55	1
56	1
57	7
58	21
59	40
60	61
61	75
62	88
63	114
64	122
65	134
66	137
67	118
68	127
69	101
70	99
71	69
72	68
73	41
74	38
75	19
76	17
77	5
78	5
79	0
80	1