A274742 - cp's OEIS frontend

A274742 Triangle read by rows: T(n,k) (n>=3, 0<=k<=n-3) = number of n-sequences of 0's and 1's that begin with 1 and have exactly one pair of adjacent 0's and exactly k pairs of adjacent 1's.

n	a(n)
3	1
4	1
5	1
6	2
7	2
8	1
9	2
10	4
11	3
12	1
13	3
14	6
15	6
16	4
17	1
18	3
19	9
20	12
21	8
22	5
23	1
24	4
25	12
26	18
27	20
28	10
29	6
30	1
31	4
32	16
33	30
34	30
35	30
36	12
37	7
38	1
39	5
40	20
41	40
42	60
43	45
44	42
45	14
46	8
47	1
48	5
49	25
50	60
51	80
52	105
53	63
54	56
55	16
56	9
57	1
58	6
59	30
60	75
61	140
62	140
63	168
64	84
65	72
66	18
67	10
68	1
69	6
70	36
71	105
72	175
73	280
74	224
75	252
76	108
77	90
78	20
79	11
80	1
81	7
82	42
83	126
84	280
85	350
86	504
87	336
88	360
89	135
90	110
91	22
92	12
93	1

[1, 1, 1, 2, 2, 1, 2, 4, 3, 1, 3, 6, 6, 4, 1, 3, 9, 12, 8, 5, 1, 4, 12, 18, 20, 10, 6, 1, 4, 16, 30, 30, 30, 12, 7, 1, 5, 20, 40, 60, 45, 42, 14, 8, 1, 5, 25, 60, 80, 105, 63, 56, 16, 9, 1, 6, 30, 75, 140, 140, 168, 84, 72, 18, 10, 1, 6, 36, 105, 175, 280, 224, 252, 108, 90, 20, 11, 1, 7, 42, 126, 280, 350, 504, 336, 360, 135, 110, 22, 12, 1]

cp's OEIS Frontend

A274742 Triangle read by rows: T(n,k) (n>=3, 0<=k<=n-3) = number of n-sequences of 0's and 1's that begin with 1 and have exactly one pair of adjacent 0's and exactly k pairs of adjacent 1's.

Table of values

List of values

n	a(n)
3	1
4	1
5	1
6	2
7	2
8	1
9	2
10	4
11	3
12	1
13	3
14	6
15	6
16	4
17	1
18	3
19	9
20	12
21	8
22	5
23	1
24	4
25	12
26	18
27	20
28	10
29	6
30	1
31	4
32	16
33	30
34	30
35	30
36	12
37	7
38	1
39	5
40	20
41	40
42	60
43	45
44	42
45	14
46	8
47	1
48	5
49	25
50	60
51	80
52	105
53	63
54	56
55	16
56	9
57	1
58	6
59	30
60	75
61	140
62	140
63	168
64	84
65	72
66	18
67	10
68	1
69	6
70	36
71	105
72	175
73	280
74	224
75	252
76	108
77	90
78	20
79	11
80	1
81	7
82	42
83	126
84	280
85	350
86	504
87	336
88	360
89	135
90	110
91	22
92	12
93	1

n	a(n)
3	1
4	1
5	1
6	2
7	2
8	1
9	2
10	4
11	3
12	1
13	3
14	6
15	6
16	4
17	1
18	3
19	9
20	12
21	8
22	5
23	1
24	4
25	12
26	18
27	20
28	10
29	6
30	1
31	4
32	16
33	30
34	30
35	30
36	12
37	7
38	1
39	5
40	20
41	40
42	60
43	45
44	42
45	14
46	8
47	1
48	5
49	25
50	60
51	80
52	105
53	63
54	56
55	16
56	9
57	1
58	6
59	30
60	75
61	140
62	140
63	168
64	84
65	72
66	18
67	10
68	1
69	6
70	36
71	105
72	175
73	280
74	224
75	252
76	108
77	90
78	20
79	11
80	1
81	7
82	42
83	126
84	280
85	350
86	504
87	336
88	360
89	135
90	110
91	22
92	12
93	1

n	a(n)
3	1
4	1
5	1
6	2
7	2
8	1
9	2
10	4
11	3
12	1
13	3
14	6
15	6
16	4
17	1
18	3
19	9
20	12
21	8
22	5
23	1
24	4
25	12
26	18
27	20
28	10
29	6
30	1
31	4
32	16
33	30
34	30
35	30
36	12
37	7
38	1
39	5
40	20
41	40
42	60
43	45
44	42
45	14
46	8
47	1
48	5
49	25
50	60
51	80
52	105
53	63
54	56
55	16
56	9
57	1
58	6
59	30
60	75
61	140
62	140
63	168
64	84
65	72
66	18
67	10
68	1
69	6
70	36
71	105
72	175
73	280
74	224
75	252
76	108
77	90
78	20
79	11
80	1
81	7
82	42
83	126
84	280
85	350
86	504
87	336
88	360
89	135
90	110
91	22
92	12
93	1