A332752 - OEIS

%I #24 Sep 27 2023 18:30:10

%S 1,1,4,16,110,544,5444,32520,385776,3282108,40916528,354328560,

%T 7200045216,67347823160,1182323197504,18086875471594,358787259407482,

%U 4564034487662420

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

%e In case of n = 1.

%e      |              | b(1)

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

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

%e In case of n = 2.

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

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

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

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

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

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

%e In case of n = 3.

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

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

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

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

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

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

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

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

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

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

%e    9 | [2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3] | [2, 2, 2]

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

%e   11 | [2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1, 1] | [0, 0, 0]

%e   12 | [1, 1, 1, 1, 3, 3, 3, 3, 2, 2, 2, 2] | [0, 0, 0]

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

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

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

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

%e * (strongly decreasing)

%Y Column 4 of A332762.

%Y Cf. A104430, A261517 (strongly decreasing), A285698, A322178, A332748, A332773, A332783, A332784.

%K nonn,more

%O 0,3

%A _Seiichi Manyama_, Feb 22 2020

%E a(10)-a(17) from _Max Alekseyev_, Sep 27 2023