A118344 - cp's OEIS frontend

A118344 Pendular Catalan triangle, read by rows, where row n is formed from row n-1 by the recurrence: if n > 2k, T(n,k) = T(n,n-k) + T(n-1,k), else T(n,k) = T(n,n-1-k) - T(n-1,k) - T(n-1,k+1), for n>=k>=0, with T(n,0)=1 and T(n,n)=0^n.

n	a(n)
0	1
1	1
2	0
3	1
4	1
5	0
6	1
7	2
8	1
9	0
10	1
11	3
12	2
13	1
14	0
15	1
16	4
17	5
18	3
19	1
20	0
21	1
22	5
23	9
24	5
25	4
26	1
27	0
28	1
29	6
30	14
31	14
32	9
33	5
34	1
35	0
36	1
37	7
38	20
39	28
40	14
41	14
42	6
43	1
44	0
45	1
46	8
47	27
48	48
49	42
50	28
51	20
52	7
53	1
54	0
55	1
56	9
57	35
58	75
59	90
60	42
61	48
62	27
63	8
64	1
65	0
66	1
67	10
68	44
69	110
70	165
71	132
72	90
73	75
74	35
75	9
76	1
77	0
78	1
79	11
80	54
81	154
82	275
83	297
84	132
85	165
86	110
87	44
88	10
89	1
90	0

[1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 2, 1, 0, 1, 4, 5, 3, 1, 0, 1, 5, 9, 5, 4, 1, 0, 1, 6, 14, 14, 9, 5, 1, 0, 1, 7, 20, 28, 14, 14, 6, 1, 0, 1, 8, 27, 48, 42, 28, 20, 7, 1, 0, 1, 9, 35, 75, 90, 42, 48, 27, 8, 1, 0, 1, 10, 44, 110, 165, 132, 90, 75, 35, 9, 1, 0, 1, 11, 54, 154, 275, 297, 132, 165, 110, 44, 10, 1, 0]

cp's OEIS Frontend

A118344 Pendular Catalan triangle, read by rows, where row n is formed from row n-1 by the recurrence: if n > 2k, T(n,k) = T(n,n-k) + T(n-1,k), else T(n,k) = T(n,n-1-k) - T(n-1,k) - T(n-1,k+1), for n>=k>=0, with T(n,0)=1 and T(n,n)=0^n.

Table of values

List of values

n	a(n)
0	1
1	1
2	0
3	1
4	1
5	0
6	1
7	2
8	1
9	0
10	1
11	3
12	2
13	1
14	0
15	1
16	4
17	5
18	3
19	1
20	0
21	1
22	5
23	9
24	5
25	4
26	1
27	0
28	1
29	6
30	14
31	14
32	9
33	5
34	1
35	0
36	1
37	7
38	20
39	28
40	14
41	14
42	6
43	1
44	0
45	1
46	8
47	27
48	48
49	42
50	28
51	20
52	7
53	1
54	0
55	1
56	9
57	35
58	75
59	90
60	42
61	48
62	27
63	8
64	1
65	0
66	1
67	10
68	44
69	110
70	165
71	132
72	90
73	75
74	35
75	9
76	1
77	0
78	1
79	11
80	54
81	154
82	275
83	297
84	132
85	165
86	110
87	44
88	10
89	1
90	0

n	a(n)
0	1
1	1
2	0
3	1
4	1
5	0
6	1
7	2
8	1
9	0
10	1
11	3
12	2
13	1
14	0
15	1
16	4
17	5
18	3
19	1
20	0
21	1
22	5
23	9
24	5
25	4
26	1
27	0
28	1
29	6
30	14
31	14
32	9
33	5
34	1
35	0
36	1
37	7
38	20
39	28
40	14
41	14
42	6
43	1
44	0
45	1
46	8
47	27
48	48
49	42
50	28
51	20
52	7
53	1
54	0
55	1
56	9
57	35
58	75
59	90
60	42
61	48
62	27
63	8
64	1
65	0
66	1
67	10
68	44
69	110
70	165
71	132
72	90
73	75
74	35
75	9
76	1
77	0
78	1
79	11
80	54
81	154
82	275
83	297
84	132
85	165
86	110
87	44
88	10
89	1
90	0

n	a(n)
0	1
1	1
2	0
3	1
4	1
5	0
6	1
7	2
8	1
9	0
10	1
11	3
12	2
13	1
14	0
15	1
16	4
17	5
18	3
19	1
20	0
21	1
22	5
23	9
24	5
25	4
26	1
27	0
28	1
29	6
30	14
31	14
32	9
33	5
34	1
35	0
36	1
37	7
38	20
39	28
40	14
41	14
42	6
43	1
44	0
45	1
46	8
47	27
48	48
49	42
50	28
51	20
52	7
53	1
54	0
55	1
56	9
57	35
58	75
59	90
60	42
61	48
62	27
63	8
64	1
65	0
66	1
67	10
68	44
69	110
70	165
71	132
72	90
73	75
74	35
75	9
76	1
77	0
78	1
79	11
80	54
81	154
82	275
83	297
84	132
85	165
86	110
87	44
88	10
89	1
90	0