A097567 - cp's OEIS frontend

A097567 T(n,k)= count of partitions p such that Abs( Odd(p)-Odd(p') ) = k, where p' is the transpose of p and Odd(p) counts the odd elements in p. Related to Stanley's 'f'.

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

[1, 1, 0, 0, 0, 2, 1, 0, 2, 0, 3, 0, 0, 0, 2, 3, 0, 2, 0, 2, 0, 1, 0, 8, 0, 0, 0, 2, 3, 0, 8, 0, 2, 0, 2, 0, 10, 0, 2, 0, 8, 0, 0, 0, 2, 10, 0, 8, 0, 8, 0, 2, 0, 2, 0, 4, 0, 26, 0, 2, 0, 8, 0, 0, 0, 2, 10, 0, 26, 0, 8, 0, 8, 0, 2, 0, 2, 0, 27, 0, 10, 0, 28, 0, 2, 0, 8, 0, 0, 0, 2, 27, 0, 26, 0, 28, 0, 8, 0, 8]

cp's OEIS Frontend

A097567 T(n,k)= count of partitions p such that Abs( Odd(p)-Odd(p') ) = k, where p' is the transpose of p and Odd(p) counts the odd elements in p. Related to Stanley's 'f'.

Table of values

List of values

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

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

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