A332748 The number of permutations of {1,1,1,2,2,2,...,n,n,n} such that each triple of k's (k=1..n) is equally spaced with b(k) other elements in between and b(1) >= b(2) >= ... >= b(n).

1, 1, 4, 18, 124, 738, 7464, 55890, 668778, 7030210, 90713844, 1054221258, 18597735744, 242795838520

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Example

n = 1 case:
     |           | b(1)
-----+-----------+------
   1 | [1, 1, 1] | [0] *
.
n = 2 case:
     |                    | b(1),b(2)
-----+--------------------+----------
   1 | [2, 2, 2, 1, 1, 1] | [0, 0]
   2 | [2, 1, 2, 1, 2, 1] | [1, 1]
   3 | [1, 2, 1, 2, 1, 2] | [1, 1]
   4 | [1, 1, 1, 2, 2, 2] | [0, 0]
.
n = 3 case:
     |                             | 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]
* (strongly decreasing)

Crossrefs

Column k=3 of A332762.

Cf. A104429, A059108, A261516 (strongly decreasing), A322178, A332752.

Sequence in context: A292500 A228065 A317377 * A215691 A359460 A073511

Adjacent sequences: A332745 A332746 A332747 * A332749 A332750 A332751

Keyword

nonn,more

Author

Seiichi Manyama, Feb 21 2020

Extensions

a(10)-a(13) from Max Alekseyev, Sep 26 2023

Status

approved