login
A332752
The number of permutations of {1,1,1,1,2,2,2,2,...,n,n,n,n} such that each quadruple of k's (k=1..n) is equally spaced with b(k) other elements in between, and b(1) >= b(2) >= ... >= b(n).
5
1, 1, 4, 16, 110, 544, 5444, 32520, 385776, 3282108, 40916528, 354328560, 7200045216, 67347823160, 1182323197504, 18086875471594, 358787259407482, 4564034487662420
OFFSET
0,3
EXAMPLE
In case of n = 1.
| | b(1)
-----+--------------+------
1 | [1, 1, 1, 1] | [0] *
In case of n = 2.
| | b(1),b(2)
-----+--------------------------+----------
1 | [2, 2, 2, 2, 1, 1, 1, 1] | [0, 0]
2 | [2, 1, 2, 1, 2, 1, 2, 1] | [1, 1]
3 | [1, 2, 1, 2, 1, 2, 1, 2] | [1, 1]
4 | [1, 1, 1, 1, 2, 2, 2, 2] | [0, 0]
In case of n = 3.
| | b(1),b(2),b(3)
-----+--------------------------------------+---------------
1 | [3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1] | [0, 0, 0]
2 | [3, 3, 3, 3, 2, 1, 2, 1, 2, 1, 2, 1] | [1, 1, 0]
3 | [3, 3, 3, 3, 1, 2, 1, 2, 1, 2, 1, 2] | [1, 1, 0]
4 | [3, 3, 3, 3, 1, 1, 1, 1, 2, 2, 2, 2] | [0, 0, 0]
5 | [3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1] | [2, 2, 2]
6 | [3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2] | [2, 2, 2]
7 | [2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1] | [2, 2, 2]
8 | [1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2] | [2, 2, 2]
9 | [2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3] | [2, 2, 2]
10 | [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3] | [2, 2, 2]
11 | [2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1, 1] | [0, 0, 0]
12 | [1, 1, 1, 1, 3, 3, 3, 3, 2, 2, 2, 2] | [0, 0, 0]
13 | [2, 2, 2, 2, 1, 1, 1, 1, 3, 3, 3, 3] | [0, 0, 0]
14 | [2, 1, 2, 1, 2, 1, 2, 1, 3, 3, 3, 3] | [1, 1, 0]
15 | [1, 2, 1, 2, 1, 2, 1, 2, 3, 3, 3, 3] | [1, 1, 0]
16 | [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3] | [0, 0, 0]
* (strongly decreasing)
CROSSREFS
Column 4 of A332762.
Cf. A104430, A261517 (strongly decreasing), A285698, A322178, A332748, A332773, A332783, A332784.
Sequence in context: A131043 A071554 A212313 * A356130 A210573 A337040
KEYWORD
nonn,more
AUTHOR
Seiichi Manyama, Feb 22 2020
EXTENSIONS
a(10)-a(17) from Max Alekseyev, Sep 27 2023
STATUS
approved