A097994 - cp's OEIS frontend

A097994 T(n,k) counts plane partitions of n that can be 'extended' in (k+2) ways to a plane partition of n+1 by adding 1 element to it. Equivalently, it counts how many partitions of n have (k+2) different partitions of n+1 just covering it.

n	a(n)
1	1
2	3
3	0
4	3
5	3
6	0
7	6
8	6
9	0
10	1
11	3
12	15
13	3
14	3
15	0
16	9
17	21
18	6
19	12
20	0
21	0
22	3
23	34
24	21
25	25
26	3
27	0
28	0
29	10
30	45
31	36
32	54
33	15
34	0
35	0
36	0
37	6
38	54
39	72
40	108
41	36
42	6
43	0
44	0
45	0
46	9
47	84
48	102
49	172
50	117
51	15
52	0
53	1
54	0
55	0
56	3
57	84
58	174
59	306
60	228
61	54
62	7
63	3
64	0
65	0
66	0
67	18
68	114
69	225
70	483
71	447
72	162
73	18
74	12
75	0
76	0
77	0
78	0
79	3
80	114

[1, 3, 0, 3, 3, 0, 6, 6, 0, 1, 3, 15, 3, 3, 0, 9, 21, 6, 12, 0, 0, 3, 34, 21, 25, 3, 0, 0, 10, 45, 36, 54, 15, 0, 0, 0, 6, 54, 72, 108, 36, 6, 0, 0, 0, 9, 84, 102, 172, 117, 15, 0, 1, 0, 0, 3, 84, 174, 306, 228, 54, 7, 3, 0, 0, 0, 18, 114, 225, 483, 447, 162, 18, 12, 0, 0, 0, 0, 3, 114]

cp's OEIS Frontend

A097994 T(n,k) counts plane partitions of n that can be 'extended' in (k+2) ways to a plane partition of n+1 by adding 1 element to it. Equivalently, it counts how many partitions of n have (k+2) different partitions of n+1 just covering it.

Table of values

List of values

n	a(n)
1	1
2	3
3	0
4	3
5	3
6	0
7	6
8	6
9	0
10	1
11	3
12	15
13	3
14	3
15	0
16	9
17	21
18	6
19	12
20	0
21	0
22	3
23	34
24	21
25	25
26	3
27	0
28	0
29	10
30	45
31	36
32	54
33	15
34	0
35	0
36	0
37	6
38	54
39	72
40	108
41	36
42	6
43	0
44	0
45	0
46	9
47	84
48	102
49	172
50	117
51	15
52	0
53	1
54	0
55	0
56	3
57	84
58	174
59	306
60	228
61	54
62	7
63	3
64	0
65	0
66	0
67	18
68	114
69	225
70	483
71	447
72	162
73	18
74	12
75	0
76	0
77	0
78	0
79	3
80	114

n	a(n)
1	1
2	3
3	0
4	3
5	3
6	0
7	6
8	6
9	0
10	1
11	3
12	15
13	3
14	3
15	0
16	9
17	21
18	6
19	12
20	0
21	0
22	3
23	34
24	21
25	25
26	3
27	0
28	0
29	10
30	45
31	36
32	54
33	15
34	0
35	0
36	0
37	6
38	54
39	72
40	108
41	36
42	6
43	0
44	0
45	0
46	9
47	84
48	102
49	172
50	117
51	15
52	0
53	1
54	0
55	0
56	3
57	84
58	174
59	306
60	228
61	54
62	7
63	3
64	0
65	0
66	0
67	18
68	114
69	225
70	483
71	447
72	162
73	18
74	12
75	0
76	0
77	0
78	0
79	3
80	114

n	a(n)
1	1
2	3
3	0
4	3
5	3
6	0
7	6
8	6
9	0
10	1
11	3
12	15
13	3
14	3
15	0
16	9
17	21
18	6
19	12
20	0
21	0
22	3
23	34
24	21
25	25
26	3
27	0
28	0
29	10
30	45
31	36
32	54
33	15
34	0
35	0
36	0
37	6
38	54
39	72
40	108
41	36
42	6
43	0
44	0
45	0
46	9
47	84
48	102
49	172
50	117
51	15
52	0
53	1
54	0
55	0
56	3
57	84
58	174
59	306
60	228
61	54
62	7
63	3
64	0
65	0
66	0
67	18
68	114
69	225
70	483
71	447
72	162
73	18
74	12
75	0
76	0
77	0
78	0
79	3
80	114