A332773 The number of permutations of {1,1,1,1,1,2,2,2,2,2,...,n,n,n,n,n} with the property that b(1) >= b(2) >= ... >= b(n), where five k's are skipped by b(k) for k=1..n.

1, 1, 4, 16, 104, 508, 5136, 28224, 333360, 2793888, 34010208, 276522240, 5903380896, 50068045536, 892740867024, 13555604385504, 260760485969664, 3084227796562768, 91112167715233008, 1145087508241888160

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Example

In case of n = 1.
     |                 | b(1)
-----+-----------------+-----
   1 | [1, 1, 1, 1, 1] | [0]
In case of n = 2.
     |                                | b(1),b(2)
-----+--------------------------------+----------
   1 | [2, 2, 2, 2, 2, 1, 1, 1, 1, 1] | [0, 0]
   2 | [2, 1, 2, 1, 2, 1, 2, 1, 2, 1] | [1, 1]
   3 | [1, 2, 1, 2, 1, 2, 1, 2, 1, 2] | [1, 1]
   4 | [1, 1, 1, 1, 1, 2, 2, 2, 2, 2] | [0, 0]
In case of n = 3.
     |                                               | b(1),b(2),b(3)
-----+-----------------------------------------------+---------------
   1 | [3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1] | [0, 0, 0]
   2 | [3, 3, 3, 3, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1] | [1, 1, 0]
   3 | [3, 3, 3, 3, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2] | [1, 1, 0]
   4 | [3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2] | [0, 0, 0]
   5 | [3, 2, 1, 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, 3, 1, 2] | [2, 2, 2]
   7 | [2, 3, 1, 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, 1, 3, 2] | [2, 2, 2]
   9 | [2, 1, 3, 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, 1, 2, 3] | [2, 2, 2]
  11 | [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1] | [0, 0, 0]
  12 | [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2] | [0, 0, 0]
  13 | [2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3] | [0, 0, 0]
  14 | [2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 3, 3, 3, 3] | [1, 1, 0]
  15 | [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 3, 3, 3, 3] | [1, 1, 0]
  16 | [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3] | [0, 0, 0]

Crossrefs

Column 5 of A332762.

Cf. A104431, A322178, A332748, A332752, A332783, A332784.

Sequence in context: A334750 A094637 A332783 * A203716 A330537 A136793

Adjacent sequences: A332770 A332771 A332772 * A332774 A332775 A332776

Keyword

nonn

Author

Seiichi Manyama, Feb 24 2020

Extensions

a(10)-a(19) from Max Alekseyev, Sep 26 2023

Status

approved