A168443 - cp's OEIS frontend

A168443 Triangle, T(n,k) = number of compositions a(1),...,a(k) of n, such that a(i+1) <= a(i) + 1 for 1 <= i < k.

n	a(n)
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	2
9	3
10	1
11	1
12	3
13	4
14	4
15	1
16	1
17	3
18	6
19	7
20	5
21	1
22	1
23	4
24	7
25	11
26	11
27	6
28	1
29	1
30	4
31	9
32	15
33	19
34	16
35	7
36	1
37	1
38	5
39	11
40	19
41	29
42	31
43	22
44	8
45	1
46	1
47	5
48	13
49	25
50	39
51	52
52	48
53	29
54	9
55	1
56	1
57	6
58	15
59	30
60	53
61	76
62	88
63	71
64	37
65	10
66	1
67	1
68	6
69	18
70	37
71	67
72	107
73	140
74	142
75	101
76	46
77	11
78	1
79	1
80	7
81	20
82	44
83	84
84	143
85	207
86	245
87	220
88	139
89	56
90	12
91	1

[1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 3, 4, 4, 1, 1, 3, 6, 7, 5, 1, 1, 4, 7, 11, 11, 6, 1, 1, 4, 9, 15, 19, 16, 7, 1, 1, 5, 11, 19, 29, 31, 22, 8, 1, 1, 5, 13, 25, 39, 52, 48, 29, 9, 1, 1, 6, 15, 30, 53, 76, 88, 71, 37, 10, 1, 1, 6, 18, 37, 67, 107, 140, 142, 101, 46, 11, 1, 1, 7, 20, 44, 84, 143, 207, 245, 220, 139, 56, 12, 1]

cp's OEIS Frontend

A168443 Triangle, T(n,k) = number of compositions a(1),...,a(k) of n, such that a(i+1) <= a(i) + 1 for 1 <= i < k.

Table of values

List of values

n	a(n)
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	2
9	3
10	1
11	1
12	3
13	4
14	4
15	1
16	1
17	3
18	6
19	7
20	5
21	1
22	1
23	4
24	7
25	11
26	11
27	6
28	1
29	1
30	4
31	9
32	15
33	19
34	16
35	7
36	1
37	1
38	5
39	11
40	19
41	29
42	31
43	22
44	8
45	1
46	1
47	5
48	13
49	25
50	39
51	52
52	48
53	29
54	9
55	1
56	1
57	6
58	15
59	30
60	53
61	76
62	88
63	71
64	37
65	10
66	1
67	1
68	6
69	18
70	37
71	67
72	107
73	140
74	142
75	101
76	46
77	11
78	1
79	1
80	7
81	20
82	44
83	84
84	143
85	207
86	245
87	220
88	139
89	56
90	12
91	1

n	a(n)
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	2
9	3
10	1
11	1
12	3
13	4
14	4
15	1
16	1
17	3
18	6
19	7
20	5
21	1
22	1
23	4
24	7
25	11
26	11
27	6
28	1
29	1
30	4
31	9
32	15
33	19
34	16
35	7
36	1
37	1
38	5
39	11
40	19
41	29
42	31
43	22
44	8
45	1
46	1
47	5
48	13
49	25
50	39
51	52
52	48
53	29
54	9
55	1
56	1
57	6
58	15
59	30
60	53
61	76
62	88
63	71
64	37
65	10
66	1
67	1
68	6
69	18
70	37
71	67
72	107
73	140
74	142
75	101
76	46
77	11
78	1
79	1
80	7
81	20
82	44
83	84
84	143
85	207
86	245
87	220
88	139
89	56
90	12
91	1

n	a(n)
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	2
9	3
10	1
11	1
12	3
13	4
14	4
15	1
16	1
17	3
18	6
19	7
20	5
21	1
22	1
23	4
24	7
25	11
26	11
27	6
28	1
29	1
30	4
31	9
32	15
33	19
34	16
35	7
36	1
37	1
38	5
39	11
40	19
41	29
42	31
43	22
44	8
45	1
46	1
47	5
48	13
49	25
50	39
51	52
52	48
53	29
54	9
55	1
56	1
57	6
58	15
59	30
60	53
61	76
62	88
63	71
64	37
65	10
66	1
67	1
68	6
69	18
70	37
71	67
72	107
73	140
74	142
75	101
76	46
77	11
78	1
79	1
80	7
81	20
82	44
83	84
84	143
85	207
86	245
87	220
88	139
89	56
90	12
91	1