A116644 - cp's OEIS frontend

A116644 Triangle read by rows: T(n,k) is the number of partitions of n having exactly k doubletons (n>=0, k>=0). By a doubleton in a partition we mean an occurrence of a part exactly twice (the partition [4,(3,3),2,2,2,(1,1)] has two doubletons, shown between parentheses).

n	a(n)
0	1
1	1
2	1
3	1
4	3
5	3
6	2
7	5
8	2
9	8
10	2
11	1
12	10
13	5
14	13
15	8
16	1
17	20
18	9
19	1
20	26
21	12
22	4
23	33
24	21
25	2
26	46
27	25
28	5
29	1
30	58
31	37
32	6
33	75
34	48
35	11
36	1
37	101
38	59
39	16
40	125
41	84
42	19
43	3
44	157
45	115
46	23
47	2
48	206
49	135
50	39
51	5
52	253
53	187
54	46
55	4
56	317
57	238
58	63
59	8
60	1
61	403
62	292
63	90
64	7
65	494
66	382
67	108
68	17
69	1
70	608
71	490
72	139
73	18

[1, 1, 1, 1, 3, 3, 2, 5, 2, 8, 2, 1, 10, 5, 13, 8, 1, 20, 9, 1, 26, 12, 4, 33, 21, 2, 46, 25, 5, 1, 58, 37, 6, 75, 48, 11, 1, 101, 59, 16, 125, 84, 19, 3, 157, 115, 23, 2, 206, 135, 39, 5, 253, 187, 46, 4, 317, 238, 63, 8, 1, 403, 292, 90, 7, 494, 382, 108, 17, 1, 608, 490, 139, 18]

cp's OEIS Frontend

A116644 Triangle read by rows: T(n,k) is the number of partitions of n having exactly k doubletons (n>=0, k>=0). By a doubleton in a partition we mean an occurrence of a part exactly twice (the partition [4,(3,3),2,2,2,(1,1)] has two doubletons, shown between parentheses).

Table of values

List of values

n	a(n)
0	1
1	1
2	1
3	1
4	3
5	3
6	2
7	5
8	2
9	8
10	2
11	1
12	10
13	5
14	13
15	8
16	1
17	20
18	9
19	1
20	26
21	12
22	4
23	33
24	21
25	2
26	46
27	25
28	5
29	1
30	58
31	37
32	6
33	75
34	48
35	11
36	1
37	101
38	59
39	16
40	125
41	84
42	19
43	3
44	157
45	115
46	23
47	2
48	206
49	135
50	39
51	5
52	253
53	187
54	46
55	4
56	317
57	238
58	63
59	8
60	1
61	403
62	292
63	90
64	7
65	494
66	382
67	108
68	17
69	1
70	608
71	490
72	139
73	18

n	a(n)
0	1
1	1
2	1
3	1
4	3
5	3
6	2
7	5
8	2
9	8
10	2
11	1
12	10
13	5
14	13
15	8
16	1
17	20
18	9
19	1
20	26
21	12
22	4
23	33
24	21
25	2
26	46
27	25
28	5
29	1
30	58
31	37
32	6
33	75
34	48
35	11
36	1
37	101
38	59
39	16
40	125
41	84
42	19
43	3
44	157
45	115
46	23
47	2
48	206
49	135
50	39
51	5
52	253
53	187
54	46
55	4
56	317
57	238
58	63
59	8
60	1
61	403
62	292
63	90
64	7
65	494
66	382
67	108
68	17
69	1
70	608
71	490
72	139
73	18

n	a(n)
0	1
1	1
2	1
3	1
4	3
5	3
6	2
7	5
8	2
9	8
10	2
11	1
12	10
13	5
14	13
15	8
16	1
17	20
18	9
19	1
20	26
21	12
22	4
23	33
24	21
25	2
26	46
27	25
28	5
29	1
30	58
31	37
32	6
33	75
34	48
35	11
36	1
37	101
38	59
39	16
40	125
41	84
42	19
43	3
44	157
45	115
46	23
47	2
48	206
49	135
50	39
51	5
52	253
53	187
54	46
55	4
56	317
57	238
58	63
59	8
60	1
61	403
62	292
63	90
64	7
65	494
66	382
67	108
68	17
69	1
70	608
71	490
72	139
73	18