A373242 - cp's OEIS frontend

A373242 T(n,k) is the sum for all integer partitions of n of length k of the difference between the number of different parts and the number of different multiplicities.

n	a(n)
1	0
2	0
3	0
4	0
5	1
6	0
7	0
8	1
9	0
10	0
11	0
12	2
13	0
14	0
15	0
16	0
17	2
18	2
19	1
20	0
21	0
22	0
23	3
24	2
25	1
26	0
27	0
28	0
29	0
30	3
31	4
32	3
33	1
34	0
35	0
36	0
37	0
38	4
39	6
40	4
41	2
42	2
43	0
44	0
45	0
46	0
47	4
48	8
49	8
50	5
51	1
52	1
53	0
54	0
55	0
56	0
57	5
58	10
59	10
60	7
61	2
62	1
63	1
64	0
65	0
66	0
67	0
68	5
69	14
70	16
71	12
72	8
73	3
74	2
75	1
76	0
77	0
78	0
79	0
80	6
81	16
82	20
83	17
84	8
85	6
86	2
87	1
88	1
89	0
90	0
91	0
92	0
93	6
94	20
95	29
96	25
97	16
98	10
99	5
100	2
101	1
102	1
103	0
104	0
105	0
106	0
107	7
108	24
109	35
110	36
111	27
112	14
113	7
114	6
115	3
116	1
117	1
118	0
119	0
120	0

[0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 3, 4, 3, 1, 0, 0, 0, 0, 4, 6, 4, 2, 2, 0, 0, 0, 0, 4, 8, 8, 5, 1, 1, 0, 0, 0, 0, 5, 10, 10, 7, 2, 1, 1, 0, 0, 0, 0, 5, 14, 16, 12, 8, 3, 2, 1, 0, 0, 0, 0, 6, 16, 20, 17, 8, 6, 2, 1, 1, 0, 0, 0, 0, 6, 20, 29, 25, 16, 10, 5, 2, 1, 1, 0, 0, 0, 0, 7, 24, 35, 36, 27, 14, 7, 6, 3, 1, 1, 0, 0, 0]

cp's OEIS Frontend

A373242 T(n,k) is the sum for all integer partitions of n of length k of the difference between the number of different parts and the number of different multiplicities.

Table of values

List of values

n	a(n)
1	0
2	0
3	0
4	0
5	1
6	0
7	0
8	1
9	0
10	0
11	0
12	2
13	0
14	0
15	0
16	0
17	2
18	2
19	1
20	0
21	0
22	0
23	3
24	2
25	1
26	0
27	0
28	0
29	0
30	3
31	4
32	3
33	1
34	0
35	0
36	0
37	0
38	4
39	6
40	4
41	2
42	2
43	0
44	0
45	0
46	0
47	4
48	8
49	8
50	5
51	1
52	1
53	0
54	0
55	0
56	0
57	5
58	10
59	10
60	7
61	2
62	1
63	1
64	0
65	0
66	0
67	0
68	5
69	14
70	16
71	12
72	8
73	3
74	2
75	1
76	0
77	0
78	0
79	0
80	6
81	16
82	20
83	17
84	8
85	6
86	2
87	1
88	1
89	0
90	0
91	0
92	0
93	6
94	20
95	29
96	25
97	16
98	10
99	5
100	2
101	1
102	1
103	0
104	0
105	0
106	0
107	7
108	24
109	35
110	36
111	27
112	14
113	7
114	6
115	3
116	1
117	1
118	0
119	0
120	0

n	a(n)
1	0
2	0
3	0
4	0
5	1
6	0
7	0
8	1
9	0
10	0
11	0
12	2
13	0
14	0
15	0
16	0
17	2
18	2
19	1
20	0
21	0
22	0
23	3
24	2
25	1
26	0
27	0
28	0
29	0
30	3
31	4
32	3
33	1
34	0
35	0
36	0
37	0
38	4
39	6
40	4
41	2
42	2
43	0
44	0
45	0
46	0
47	4
48	8
49	8
50	5
51	1
52	1
53	0
54	0
55	0
56	0
57	5
58	10
59	10
60	7
61	2
62	1
63	1
64	0
65	0
66	0
67	0
68	5
69	14
70	16
71	12
72	8
73	3
74	2
75	1
76	0
77	0
78	0
79	0
80	6
81	16
82	20
83	17
84	8
85	6
86	2
87	1
88	1
89	0
90	0
91	0
92	0
93	6
94	20
95	29
96	25
97	16
98	10
99	5
100	2
101	1
102	1
103	0
104	0
105	0
106	0
107	7
108	24
109	35
110	36
111	27
112	14
113	7
114	6
115	3
116	1
117	1
118	0
119	0
120	0

n	a(n)
1	0
2	0
3	0
4	0
5	1
6	0
7	0
8	1
9	0
10	0
11	0
12	2
13	0
14	0
15	0
16	0
17	2
18	2
19	1
20	0
21	0
22	0
23	3
24	2
25	1
26	0
27	0
28	0
29	0
30	3
31	4
32	3
33	1
34	0
35	0
36	0
37	0
38	4
39	6
40	4
41	2
42	2
43	0
44	0
45	0
46	0
47	4
48	8
49	8
50	5
51	1
52	1
53	0
54	0
55	0
56	0
57	5
58	10
59	10
60	7
61	2
62	1
63	1
64	0
65	0
66	0
67	0
68	5
69	14
70	16
71	12
72	8
73	3
74	2
75	1
76	0
77	0
78	0
79	0
80	6
81	16
82	20
83	17
84	8
85	6
86	2
87	1
88	1
89	0
90	0
91	0
92	0
93	6
94	20
95	29
96	25
97	16
98	10
99	5
100	2
101	1
102	1
103	0
104	0
105	0
106	0
107	7
108	24
109	35
110	36
111	27
112	14
113	7
114	6
115	3
116	1
117	1
118	0
119	0
120	0