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A332784
The number of permutations of {n 1's, n 2's,...,n n's} with the property that b(1) >= b(2) >= ... >= b(n), where n k's are skipped by b(k) for k=1..n.
4
5, 18, 110, 508, 4968, 25824, 305376, 2375616, 28316832, 202354752, 4771240704, 33499830528, 612464852736, 9023719675392, 176001733301760, 1649576855476224, 56693983168309248, 551579829498390528, 20888523161929138176, 342595860998544285696
OFFSET
2,1
FORMULA
Conjecture: a(n) = A332783(n) + (n-1)!.
EXAMPLE
In case of n = 2.
| | b(1),b(2)
-----+--------------+----------
1 | [2, 2, 1, 1] | [0, 0]
2 | [2, 1, 2, 1] | [1, 1]
3 | [1, 2, 2, 1] | [2, 0]
4 | [1, 2, 1, 2] | [1, 1]
5 | [1, 1, 2, 2] | [0, 0]
In case of n = 3.
| | b(1),b(2),b(3)
-----+-----------------------------+---------------
1 | [3, 3, 3, 2, 2, 2, 1, 1, 1] | [0, 0, 0]
2 | [3, 3, 3, 2, 1, 2, 1, 2, 1] | [1, 1, 0]
3 | [3, 3, 3, 1, 2, 1, 2, 1, 2] | [1, 1, 0]
4 | [3, 3, 3, 1, 1, 1, 2, 2, 2] | [0, 0, 0]
5 | [3, 2, 1, 3, 2, 1, 3, 2, 1] | [2, 2, 2]
6 | [3, 1, 2, 3, 1, 2, 3, 1, 2] | [2, 2, 2]
7 | [1, 3, 3, 3, 1, 2, 2, 2, 1] | [3, 0, 0]
8 | [2, 3, 1, 2, 3, 1, 2, 3, 1] | [2, 2, 2]
9 | [1, 3, 2, 1, 3, 2, 1, 3, 2] | [2, 2, 2]
10 | [2, 1, 3, 2, 1, 3, 2, 1, 3] | [2, 2, 2]
11 | [1, 2, 3, 1, 2, 3, 1, 2, 3] | [2, 2, 2]
12 | [2, 2, 2, 3, 3, 3, 1, 1, 1] | [0, 0, 0]
13 | [1, 1, 1, 3, 3, 3, 2, 2, 2] | [0, 0, 0]
14 | [1, 2, 2, 2, 1, 3, 3, 3, 1] | [3, 0, 0]
15 | [2, 2, 2, 1, 1, 1, 3, 3, 3] | [0, 0, 0]
16 | [2, 1, 2, 1, 2, 1, 3, 3, 3] | [1, 1, 0]
17 | [1, 2, 1, 2, 1, 2, 3, 3, 3] | [1, 1, 0]
18 | [1, 1, 1, 2, 2, 2, 3, 3, 3] | [0, 0, 0]
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 23 2020
EXTENSIONS
a(9)-a(17) from Bert Dobbelaere, Mar 08 2020
a(18)-a(21) from Max Alekseyev, Sep 26 2023
STATUS
approved