cp's OEIS Frontend

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).

%I A322178 #28 Feb 17 2020 20:53:37
%S A322178 1,1,5,33,329,3825,57293,977581,19619645,442155529,11183272973,
%T A322178 312134648549,9554405887621,317670072938621,11411690507968361,
%U A322178 440231352579839965
%N 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).
%H A322178 Edward Moody, <a href="https://github.com/EdwardMGraphite/generalised-langford">Java program for calculating entries in this sequence and A060963</a>
%e A322178 In case of n = 2.
%e A322178      |              | b(1),b(2)
%e A322178 -----+--------------+----------
%e A322178    1 | [1, 1, 2, 2] | [0, 0]
%e A322178    2 | [1, 2, 1, 2] | [1, 1]
%e A322178    3 | [1, 2, 2, 1] | [2, 0] *
%e A322178    4 | [2, 1, 2, 1] | [1, 1]
%e A322178    5 | [2, 2, 1, 1] | [0, 0]
%e A322178 In case of n = 3.
%e A322178      |                    | b(1),b(2),b(3)
%e A322178 -----+--------------------+---------------
%e A322178    1 | [1, 1, 2, 2, 3, 3] | [0, 0, 0]
%e A322178    2 | [1, 1, 3, 3, 2, 2] | [0, 0, 0]
%e A322178    3 | [1, 2, 1, 2, 3, 3] | [1, 1, 0]
%e A322178    4 | [1, 2, 2, 1, 3, 3] | [2, 0, 0]
%e A322178    5 | [1, 2, 2, 3, 3, 1] | [4, 0, 0]
%e A322178    6 | [1, 2, 3, 1, 2, 3] | [2, 2, 2]
%e A322178    7 | [1, 2, 3, 2, 3, 1] | [4, 1, 1]
%e A322178    8 | [1, 2, 3, 3, 1, 2] | [3, 3, 0]
%e A322178    9 | [1, 2, 3, 3, 2, 1] | [4, 2, 0] *
%e A322178   10 | [1, 3, 2, 1, 3, 2] | [2, 2, 2]
%e A322178   11 | [1, 3, 2, 3, 1, 2] | [3, 2, 1] *
%e A322178   12 | [1, 3, 2, 3, 2, 1] | [4, 1, 1]
%e A322178   13 | [1, 3, 3, 1, 2, 2] | [2, 0, 0]
%e A322178   14 | [1, 3, 3, 2, 1, 2] | [3, 1, 0] *
%e A322178   15 | [1, 3, 3, 2, 2, 1] | [4, 0, 0]
%e A322178   16 | [2, 1, 2, 1, 3, 3] | [1, 1, 0]
%e A322178   17 | [2, 1, 2, 3, 1, 3] | [2, 1, 1]
%e A322178   18 | [2, 1, 2, 3, 3, 1] | [3, 1, 0] *
%e A322178   19 | [2, 1, 3, 2, 1, 3] | [2, 2, 2]
%e A322178   20 | [2, 1, 3, 2, 3, 1] | [3, 2, 1] *
%e A322178   21 | [2, 1, 3, 3, 2, 1] | [3, 3, 0]
%e A322178   22 | [2, 2, 1, 1, 3, 3] | [0, 0, 0]
%e A322178   23 | [2, 2, 1, 3, 3, 1] | [2, 0, 0]
%e A322178   24 | [2, 2, 3, 3, 1, 1] | [0, 0, 0]
%e A322178   25 | [2, 3, 1, 2, 3, 1] | [2, 2, 2]
%e A322178   26 | [3, 1, 2, 3, 1, 2] | [2, 2, 2]
%e A322178   27 | [3, 1, 3, 2, 1, 2] | [2, 1, 1]
%e A322178   28 | [3, 2, 1, 3, 2, 1] | [2, 2, 2]
%e A322178   29 | [3, 3, 1, 1, 2, 2] | [0, 0, 0]
%e A322178   30 | [3, 3, 1, 2, 1, 2] | [1, 1, 0]
%e A322178   31 | [3, 3, 1, 2, 2, 1] | [2, 0, 0]
%e A322178   32 | [3, 3, 2, 1, 2, 1] | [1, 1, 0]
%e A322178   33 | [3, 3, 2, 2, 1, 1] | [0, 0, 0]
%e A322178 * (Strongly decreasing)
%Y A322178 Cf. A060963 (Strongly decreasing).
%K A322178 nonn,more
%O A322178 0,3
%A A322178 _Seiichi Manyama_, Nov 30 2018
%E A322178 a(9) from _Seiichi Manyama_, Dec 31 2019
%E A322178 a(10)-a(11) from _Giovanni Resta_, Jan 15 2020
%E A322178 a(12)-a(15) from _Edward Moody_, Feb 17 2020