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).

1, 1, 5, 33, 329, 3825, 57293, 977581, 19619645, 442155529, 11183272973, 312134648549, 9554405887621, 317670072938621, 11411690507968361, 440231352579839965

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Edward Moody, Java program for calculating entries in this sequence and A060963

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

Adjacent sequences: A322175 A322176 A322177 * A322179 A322180 A322181

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