[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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).
7
1, 1, 5, 33, 329, 3825, 57293, 977581, 19619645, 442155529, 11183272973, 312134648549, 9554405887621, 317670072938621, 11411690507968361, 440231352579839965
OFFSET
0,3
EXAMPLE
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)
CROSSREFS
Cf. A060963 (Strongly decreasing).
Sequence in context: A198079 A098460 A087618 * A134152 A140424 A295090
KEYWORD
nonn,more
AUTHOR
Seiichi Manyama, Nov 30 2018
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
STATUS
approved