A047110 - cp's OEIS frontend

A047110 Array read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and no up-step crosses the line y=2x/3. (Thus a path crosses the line only at lattice points and on right-steps.).

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	1
6	1
7	2
8	2
9	1
10	1
11	3
12	2
13	3
14	1
15	1
16	4
17	5
18	5
19	4
20	1
21	1
22	5
23	9
24	10
25	9
26	5
27	1
28	1
29	6
30	14
31	19
32	10
33	14
34	6
35	1
36	1
37	7
38	20
39	33
40	29
41	24
42	20
43	7
44	1
45	1
46	8
47	27
48	53
49	62
50	29
51	44
52	27
53	8
54	1
55	1
56	9
57	35
58	80
59	115
60	91
61	73
62	71
63	35
64	9
65	1
66	1
67	10
68	44
69	115
70	195
71	206
72	164
73	144
74	106
75	44
76	10
77	1

[1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 4, 5, 5, 4, 1, 1, 5, 9, 10, 9, 5, 1, 1, 6, 14, 19, 10, 14, 6, 1, 1, 7, 20, 33, 29, 24, 20, 7, 1, 1, 8, 27, 53, 62, 29, 44, 27, 8, 1, 1, 9, 35, 80, 115, 91, 73, 71, 35, 9, 1, 1, 10, 44, 115, 195, 206, 164, 144, 106, 44, 10, 1]

cp's OEIS Frontend

A047110 Array read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and no up-step crosses the line y=2x/3. (Thus a path crosses the line only at lattice points and on right-steps.).

Table of values

List of values

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	1
6	1
7	2
8	2
9	1
10	1
11	3
12	2
13	3
14	1
15	1
16	4
17	5
18	5
19	4
20	1
21	1
22	5
23	9
24	10
25	9
26	5
27	1
28	1
29	6
30	14
31	19
32	10
33	14
34	6
35	1
36	1
37	7
38	20
39	33
40	29
41	24
42	20
43	7
44	1
45	1
46	8
47	27
48	53
49	62
50	29
51	44
52	27
53	8
54	1
55	1
56	9
57	35
58	80
59	115
60	91
61	73
62	71
63	35
64	9
65	1
66	1
67	10
68	44
69	115
70	195
71	206
72	164
73	144
74	106
75	44
76	10
77	1

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	1
6	1
7	2
8	2
9	1
10	1
11	3
12	2
13	3
14	1
15	1
16	4
17	5
18	5
19	4
20	1
21	1
22	5
23	9
24	10
25	9
26	5
27	1
28	1
29	6
30	14
31	19
32	10
33	14
34	6
35	1
36	1
37	7
38	20
39	33
40	29
41	24
42	20
43	7
44	1
45	1
46	8
47	27
48	53
49	62
50	29
51	44
52	27
53	8
54	1
55	1
56	9
57	35
58	80
59	115
60	91
61	73
62	71
63	35
64	9
65	1
66	1
67	10
68	44
69	115
70	195
71	206
72	164
73	144
74	106
75	44
76	10
77	1

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	1
6	1
7	2
8	2
9	1
10	1
11	3
12	2
13	3
14	1
15	1
16	4
17	5
18	5
19	4
20	1
21	1
22	5
23	9
24	10
25	9
26	5
27	1
28	1
29	6
30	14
31	19
32	10
33	14
34	6
35	1
36	1
37	7
38	20
39	33
40	29
41	24
42	20
43	7
44	1
45	1
46	8
47	27
48	53
49	62
50	29
51	44
52	27
53	8
54	1
55	1
56	9
57	35
58	80
59	115
60	91
61	73
62	71
63	35
64	9
65	1
66	1
67	10
68	44
69	115
70	195
71	206
72	164
73	144
74	106
75	44
76	10
77	1