A322178 - OEIS

%I #28 Feb 17 2020 20:53:37

%S 1,1,5,33,329,3825,57293,977581,19619645,442155529,11183272973,

%T 312134648549,9554405887621,317670072938621,11411690507968361,

%U 440231352579839965

%N 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).

%H Edward Moody, <a href="https://github.com/EdwardMGraphite/generalised-langford">Java program for calculating entries in this sequence and A060963</a>

%e In case of n = 2.

%e      |              | b(1),b(2)

%e -----+--------------+----------

%e    1 | [1, 1, 2, 2] | [0, 0]

%e    2 | [1, 2, 1, 2] | [1, 1]

%e    3 | [1, 2, 2, 1] | [2, 0] *

%e    4 | [2, 1, 2, 1] | [1, 1]

%e    5 | [2, 2, 1, 1] | [0, 0]

%e In case of n = 3.

%e      |                    | b(1),b(2),b(3)

%e -----+--------------------+---------------

%e    1 | [1, 1, 2, 2, 3, 3] | [0, 0, 0]

%e    2 | [1, 1, 3, 3, 2, 2] | [0, 0, 0]

%e    3 | [1, 2, 1, 2, 3, 3] | [1, 1, 0]

%e    4 | [1, 2, 2, 1, 3, 3] | [2, 0, 0]

%e    5 | [1, 2, 2, 3, 3, 1] | [4, 0, 0]

%e    6 | [1, 2, 3, 1, 2, 3] | [2, 2, 2]

%e    7 | [1, 2, 3, 2, 3, 1] | [4, 1, 1]

%e    8 | [1, 2, 3, 3, 1, 2] | [3, 3, 0]

%e    9 | [1, 2, 3, 3, 2, 1] | [4, 2, 0] *

%e   10 | [1, 3, 2, 1, 3, 2] | [2, 2, 2]

%e   11 | [1, 3, 2, 3, 1, 2] | [3, 2, 1] *

%e   12 | [1, 3, 2, 3, 2, 1] | [4, 1, 1]

%e   13 | [1, 3, 3, 1, 2, 2] | [2, 0, 0]

%e   14 | [1, 3, 3, 2, 1, 2] | [3, 1, 0] *

%e   15 | [1, 3, 3, 2, 2, 1] | [4, 0, 0]

%e   16 | [2, 1, 2, 1, 3, 3] | [1, 1, 0]

%e   17 | [2, 1, 2, 3, 1, 3] | [2, 1, 1]

%e   18 | [2, 1, 2, 3, 3, 1] | [3, 1, 0] *

%e   19 | [2, 1, 3, 2, 1, 3] | [2, 2, 2]

%e   20 | [2, 1, 3, 2, 3, 1] | [3, 2, 1] *

%e   21 | [2, 1, 3, 3, 2, 1] | [3, 3, 0]

%e   22 | [2, 2, 1, 1, 3, 3] | [0, 0, 0]

%e   23 | [2, 2, 1, 3, 3, 1] | [2, 0, 0]

%e   24 | [2, 2, 3, 3, 1, 1] | [0, 0, 0]

%e   25 | [2, 3, 1, 2, 3, 1] | [2, 2, 2]

%e   26 | [3, 1, 2, 3, 1, 2] | [2, 2, 2]

%e   27 | [3, 1, 3, 2, 1, 2] | [2, 1, 1]

%e   28 | [3, 2, 1, 3, 2, 1] | [2, 2, 2]

%e   29 | [3, 3, 1, 1, 2, 2] | [0, 0, 0]

%e   30 | [3, 3, 1, 2, 1, 2] | [1, 1, 0]

%e   31 | [3, 3, 1, 2, 2, 1] | [2, 0, 0]

%e   32 | [3, 3, 2, 1, 2, 1] | [1, 1, 0]

%e   33 | [3, 3, 2, 2, 1, 1] | [0, 0, 0]

%e * (Strongly decreasing)

%Y Cf. A060963 (Strongly decreasing).

%K nonn,more

%O 0,3

%A _Seiichi Manyama_, Nov 30 2018

%E a(9) from _Seiichi Manyama_, Dec 31 2019

%E a(10)-a(11) from _Giovanni Resta_, Jan 15 2020

%E a(12)-a(15) from _Edward Moody_, Feb 17 2020