A322178 The number of permutations of {1,2,...,n,1,2,...,n} with the property that b(1) >= b(2) >= ... >= b(n) (there are b(k) numbers between the two k's for k=1..n).
1, 1, 5, 33, 329, 3825, 57293, 977581, 19619645, 442155529, 11183272973, 312134648549, 9554405887621, 317670072938621, 11411690507968361, 440231352579839965
Offset: 0
Examples
In case of n = 2.
| | b(1),b(2)
-----+--------------+----------
1 | [1, 1, 2, 2] | [0, 0]
2 | [1, 2, 1, 2] | [1, 1]
3 | [1, 2, 2, 1] | [2, 0] *
4 | [2, 1, 2, 1] | [1, 1]
5 | [2, 2, 1, 1] | [0, 0]
In case of n = 3.
| | b(1),b(2),b(3)
-----+--------------------+---------------
1 | [1, 1, 2, 2, 3, 3] | [0, 0, 0]
2 | [1, 1, 3, 3, 2, 2] | [0, 0, 0]
3 | [1, 2, 1, 2, 3, 3] | [1, 1, 0]
4 | [1, 2, 2, 1, 3, 3] | [2, 0, 0]
5 | [1, 2, 2, 3, 3, 1] | [4, 0, 0]
6 | [1, 2, 3, 1, 2, 3] | [2, 2, 2]
7 | [1, 2, 3, 2, 3, 1] | [4, 1, 1]
8 | [1, 2, 3, 3, 1, 2] | [3, 3, 0]
9 | [1, 2, 3, 3, 2, 1] | [4, 2, 0] *
10 | [1, 3, 2, 1, 3, 2] | [2, 2, 2]
11 | [1, 3, 2, 3, 1, 2] | [3, 2, 1] *
12 | [1, 3, 2, 3, 2, 1] | [4, 1, 1]
13 | [1, 3, 3, 1, 2, 2] | [2, 0, 0]
14 | [1, 3, 3, 2, 1, 2] | [3, 1, 0] *
15 | [1, 3, 3, 2, 2, 1] | [4, 0, 0]
16 | [2, 1, 2, 1, 3, 3] | [1, 1, 0]
17 | [2, 1, 2, 3, 1, 3] | [2, 1, 1]
18 | [2, 1, 2, 3, 3, 1] | [3, 1, 0] *
19 | [2, 1, 3, 2, 1, 3] | [2, 2, 2]
20 | [2, 1, 3, 2, 3, 1] | [3, 2, 1] *
21 | [2, 1, 3, 3, 2, 1] | [3, 3, 0]
22 | [2, 2, 1, 1, 3, 3] | [0, 0, 0]
23 | [2, 2, 1, 3, 3, 1] | [2, 0, 0]
24 | [2, 2, 3, 3, 1, 1] | [0, 0, 0]
25 | [2, 3, 1, 2, 3, 1] | [2, 2, 2]
26 | [3, 1, 2, 3, 1, 2] | [2, 2, 2]
27 | [3, 1, 3, 2, 1, 2] | [2, 1, 1]
28 | [3, 2, 1, 3, 2, 1] | [2, 2, 2]
29 | [3, 3, 1, 1, 2, 2] | [0, 0, 0]
30 | [3, 3, 1, 2, 1, 2] | [1, 1, 0]
31 | [3, 3, 1, 2, 2, 1] | [2, 0, 0]
32 | [3, 3, 2, 1, 2, 1] | [1, 1, 0]
33 | [3, 3, 2, 2, 1, 1] | [0, 0, 0]
* (Strongly decreasing)
Links
Crossrefs
Cf. A060963 (Strongly decreasing).
Extensions
a(9) from Seiichi Manyama, Dec 31 2019
a(10)-a(11) from Giovanni Resta, Jan 15 2020
a(12)-a(15) from Edward Moody, Feb 17 2020