|
Partitions as integers (A194602) thin fat |
Partitions with addends ≥ 2 3 4 5 6 7 8 |
Numbers of partitions of n with addends ≥ k (A026807) full half |
|
(1, 1)
1 |
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|
(2, 1)
2 |
(2, 2)
1 |
||||||||||||||||||||||||||||
|
(3, 1)
3 |
(3, 2)
1 |
(3, 3)
1 |
|||||||||||||||||||||||||||
|
(4, 1)
5 |
(4, 2)
2 |
(4, 3)
1 |
(4, 4)
1 |
||||||||||||||||||||||||||
|
(5, 1)
7 |
(5, 2)
2 |
(5, 3)
1 |
(5, 4)
1 |
(5, 5)
1 |
|||||||||||||||||||||||||
|
(6, 1)
11 |
(6, 2)
4 |
(6, 3)
2 |
(6, 4)
1 |
(6, 5)
1 |
(6, 6)
1 |
||||||||||||||||||||||||
|
(7, 1)
15 |
(7, 2)
4 |
(7, 3)
2 |
(7, 4)
1 |
(7, 5)
1 |
(7, 6)
1 |
(7, 7)
1 |
|||||||||||||||||||||||
|
(8, 1)
22 |
(8, 2)
7 |
(8, 3)
3 |
(8, 4)
2 |
(8, 5)
1 |
(8, 6)
1 |
(8, 7)
1 |
(8, 8)
1 |
||||||||||||||||||||||
|
(9, 1)
30 |
(9, 2)
8 |
(9, 3)
4 |
(9, 4)
2 |
(9, 5)
1 |
(9, 6)
1 |
(9, 7)
1 |
(9, 8)
1 |
(9, 9)
1 |
|||||||||||||||||||||
|
(10, 1)
42 |
(10, 2)
12 |
(10, 3)
5 |
(10, 4)
3 |
(10, 5)
2 |
(10, 6)
1 |
(10, 7)
1 |
(10, 8)
1 |
(10, 9)
1 |
(10, 10)
1 |
||||||||||||||||||||
|
(11, 1)
56 |
(11, 2)
14 |
(11, 3)
6 |
(11, 4)
3 |
(11, 5)
2 |
(11, 6)
1 |
(11, 7)
1 |
(11, 8)
1 |
(11, 9)
1 |
(11, 10)
1 |
(11, 11)
1 |
|||||||||||||||||||
|
(12, 1)
77 |
(12, 2)
21 |
(12, 3)
9 |
(12, 4)
5 |
(12, 5)
3 |
(12, 6)
2 |
(12, 7)
1 |
(12, 8)
1 |
(12, 9)
1 |
(12, 10)
1 |
(12, 11)
1 |
(12, 12)
1 |
||||||||||||||||||
|
(13, 1)
101 |
(13, 2)
24 |
(13, 3)
10 |
(13, 4)
5 |
(13, 5)
3 |
(13, 6)
2 |
(13, 7)
1 |
(13, 8)
1 |
(13, 9)
1 |
(13, 10)
1 |
(13, 11)
1 |
(13, 12)
1 |
(13, 13)
1 |
|||||||||||||||||
|
(14, 1)
135 |
(14, 2)
34 |
(14, 3)
13 |
(14, 4)
7 |
(14, 5)
4 |
(14, 6)
3 |
(14, 7)
2 |
(14, 8)
1 |
(14, 9)
1 |
(14, 10)
1 |
(14, 11)
1 |
(14, 12)
1 |
(14, 13)
1 |
(14, 14)
1 |
||||||||||||||||
|
(15, 1)
176 |
(15, 2)
41 |
(15, 3)
17 |
(15, 4)
8 |
(15, 5)
5 |
(15, 6)
3 |
(15, 7)
2 |
(15, 8)
1 |
(15, 9)
1 |
(15, 10)
1 |
(15, 11)
1 |
(15, 12)
1 |
(15, 13)
1 |
(15, 14)
1 |
(15, 15)
1 |
|||||||||||||||
|
(16, 1)
231 |
(16, 2)
55 |
(16, 3)
21 |
(16, 4)
11 |
(16, 5)
6 |
(16, 6)
4 |
(16, 7)
3 |
(16, 8)
2 |
(16, 9)
1 |
(16, 10)
1 |
(16, 11)
1 |
(16, 12)
1 |
(16, 13)
1 |
(16, 14)
1 |
(16, 15)
1 |
(16, 16)
1 |
||||||||||||||
|
(17, 1)
297 |
(17, 2)
66 |
(17, 3)
25 |
(17, 4)
12 |
(17, 5)
7 |
(17, 6)
4 |
(17, 7)
3 |
(17, 8)
2 |
(17, 9)
1 |
(17, 10)
1 |
(17, 11)
1 |
(17, 12)
1 |
(17, 13)
1 |
(17, 14)
1 |
(17, 15)
1 |
(17, 16)
1 |
(17, 17)
1 |
|||||||||||||
|
(18, 1)
385 |
(18, 2)
88 |
(18, 3)
33 |
(18, 4)
16 |
(18, 5)
9 |
(18, 6)
6 |
(18, 7)
4 |
(18, 8)
3 |
(18, 9)
2 |
(18, 10)
1 |
(18, 11)
1 |
(18, 12)
1 |
(18, 13)
1 |
(18, 14)
1 |
(18, 15)
1 |
(18, 16)
1 |
(18, 17)
1 |
(18, 18)
1 |
||||||||||||
|
(19, 1)
490 |
(19, 2)
105 |
(19, 3)
39 |
(19, 4)
18 |
(19, 5)
10 |
(19, 6)
6 |
(19, 7)
4 |
(19, 8)
3 |
(19, 9)
2 |
(19, 10)
1 |
(19, 11)
1 |
(19, 12)
1 |
(19, 13)
1 |
(19, 14)
1 |
(19, 15)
1 |
(19, 16)
1 |
(19, 17)
1 |
(19, 18)
1 |
(19, 19)
1 |
|||||||||||
|
(20, 1)
627 |
(20, 2)
137 |
(20, 3)
49 |
(20, 4)
24 |
(20, 5)
13 |
(20, 6)
8 |
(20, 7)
5 |
(20, 8)
4 |
(20, 9)
3 |
(20, 10)
2 |
(20, 11)
1 |
(20, 12)
1 |
(20, 13)
1 |
(20, 14)
1 |
(20, 15)
1 |
(20, 16)
1 |
(20, 17)
1 |
(20, 18)
1 |
(20, 19)
1 |
(20, 20)
1 |
||||||||||
|
(21, 1)
792 |
(21, 2)
165 |
(21, 3)
60 |
(21, 4)
27 |
(21, 5)
15 |
(21, 6)
9 |
(21, 7)
6 |
(21, 8)
4 |
(21, 9)
3 |
(21, 10)
2 |
(21, 11)
1 |
(21, 12)
1 |
(21, 13)
1 |
(21, 14)
1 |
(21, 15)
1 |
(21, 16)
1 |
(21, 17)
1 |
(21, 18)
1 |
(21, 19)
1 |
(21, 20)
1 |
(21, 21)
1 |
|||||||||
|
(22, 1)
1002 |
(22, 2)
210 |
(22, 3)
73 |
(22, 4)
34 |
(22, 5)
18 |
(22, 6)
11 |
(22, 7)
7 |
(22, 8)
5 |
(22, 9)
4 |
(22, 10)
3 |
(22, 11)
2 |
(22, 12)
1 |
(22, 13)
1 |
(22, 14)
1 |
(22, 15)
1 |
(22, 16)
1 |
(22, 17)
1 |
(22, 18)
1 |
(22, 19)
1 |
(22, 20)
1 |
(22, 21)
1 |
(22, 22)
1 |
||||||||
|
(23, 1)
1255 |
(23, 2)
253 |
(23, 3)
88 |
(23, 4)
39 |
(23, 5)
21 |
(23, 6)
12 |
(23, 7)
8 |
(23, 8)
5 |
(23, 9)
4 |
(23, 10)
3 |
(23, 11)
2 |
(23, 12)
1 |
(23, 13)
1 |
(23, 14)
1 |
(23, 15)
1 |
(23, 16)
1 |
(23, 17)
1 |
(23, 18)
1 |
(23, 19)
1 |
(23, 20)
1 |
(23, 21)
1 |
(23, 22)
1 |
(23, 23)
1 |
|||||||
|
(24, 1)
1575 |
(24, 2)
320 |
(24, 3)
110 |
(24, 4)
50 |
(24, 5)
26 |
(24, 6)
16 |
(24, 7)
10 |
(24, 8)
7 |
(24, 9)
5 |
(24, 10)
4 |
(24, 11)
3 |
(24, 12)
2 |
(24, 13)
1 |
(24, 14)
1 |
(24, 15)
1 |
(24, 16)
1 |
(24, 17)
1 |
(24, 18)
1 |
(24, 19)
1 |
(24, 20)
1 |
(24, 21)
1 |
(24, 22)
1 |
(24, 23)
1 |
(24, 24)
1 |
||||||
|
(25, 1)
1958 |
(25, 2)
383 |
(25, 3)
130 |
(25, 4)
57 |
(25, 5)
30 |
(25, 6)
17 |
(25, 7)
11 |
(25, 8)
7 |
(25, 9)
5 |
(25, 10)
4 |
(25, 11)
3 |
(25, 12)
2 |
(25, 13)
1 |
(25, 14)
1 |
(25, 15)
1 |
(25, 16)
1 |
(25, 17)
1 |
(25, 18)
1 |
(25, 19)
1 |
(25, 20)
1 |
(25, 21)
1 |
(25, 22)
1 |
(25, 23)
1 |
(25, 24)
1 |
(25, 25)
1 |
|||||
|
(26, 1)
2436 |
(26, 2)
478 |
(26, 3)
158 |
(26, 4)
70 |
(26, 5)
36 |
(26, 6)
21 |
(26, 7)
13 |
(26, 8)
9 |
(26, 9)
6 |
(26, 10)
5 |
(26, 11)
4 |
(26, 12)
3 |
(26, 13)
2 |
(26, 14)
1 |
(26, 15)
1 |
(26, 16)
1 |
(26, 17)
1 |
(26, 18)
1 |
(26, 19)
1 |
(26, 20)
1 |
(26, 21)
1 |
(26, 22)
1 |
(26, 23)
1 |
(26, 24)
1 |
(26, 25)
1 |
(26, 26)
1 |
||||
|
(27, 1)
3010 |
(27, 2)
574 |
(27, 3)
191 |
(27, 4)
81 |
(27, 5)
42 |
(27, 6)
24 |
(27, 7)
15 |
(27, 8)
10 |
(27, 9)
7 |
(27, 10)
5 |
(27, 11)
4 |
(27, 12)
3 |
(27, 13)
2 |
(27, 14)
1 |
(27, 15)
1 |
(27, 16)
1 |
(27, 17)
1 |
(27, 18)
1 |
(27, 19)
1 |
(27, 20)
1 |
(27, 21)
1 |
(27, 22)
1 |
(27, 23)
1 |
(27, 24)
1 |
(27, 25)
1 |
(27, 26)
1 |
(27, 27)
1 |
|||
|
(28, 1)
3718 |
(28, 2)
708 |
(28, 3)
230 |
(28, 4)
100 |
(28, 5)
50 |
(28, 6)
29 |
(28, 7)
18 |
(28, 8)
12 |
(28, 9)
8 |
(28, 10)
6 |
(28, 11)
5 |
(28, 12)
4 |
(28, 13)
3 |
(28, 14)
2 |
(28, 15)
1 |
(28, 16)
1 |
(28, 17)
1 |
(28, 18)
1 |
(28, 19)
1 |
(28, 20)
1 |
(28, 21)
1 |
(28, 22)
1 |
(28, 23)
1 |
(28, 24)
1 |
(28, 25)
1 |
(28, 26)
1 |
(28, 27)
1 |
(28, 28)
1 |
||
|
(29, 1)
4565 |
(29, 2)
847 |
(29, 3)
273 |
(29, 4)
115 |
(29, 5)
58 |
(29, 6)
32 |
(29, 7)
20 |
(29, 8)
13 |
(29, 9)
9 |
(29, 10)
6 |
(29, 11)
5 |
(29, 12)
4 |
(29, 13)
3 |
(29, 14)
2 |
(29, 15)
1 |
(29, 16)
1 |
(29, 17)
1 |
(29, 18)
1 |
(29, 19)
1 |
(29, 20)
1 |
(29, 21)
1 |
(29, 22)
1 |
(29, 23)
1 |
(29, 24)
1 |
(29, 25)
1 |
(29, 26)
1 |
(29, 27)
1 |
(29, 28)
1 |
(29, 29)
1 |
|
|
(30, 1)
5604 |
(30, 2)
1039 |
(30, 3)
331 |
(30, 4)
140 |
(30, 5)
70 |
(30, 6)
40 |
(30, 7)
24 |
(30, 8)
16 |
(30, 9)
11 |
(30, 10)
8 |
(30, 11)
6 |
(30, 12)
5 |
(30, 13)
4 |
(30, 14)
3 |
(30, 15)
2 |
(30, 16)
1 |
(30, 17)
1 |
(30, 18)
1 |
(30, 19)
1 |
(30, 20)
1 |
(30, 21)
1 |
(30, 22)
1 |
(30, 23)
1 |
(30, 24)
1 |
(30, 25)
1 |
(30, 26)
1 |
(30, 27)
1 |
(30, 28)
1 |
(30, 29)
1 |
(30, 30)
1 |