A332773 - OEIS

A332773

The number of permutations of {1,1,1,1,1,2,2,2,2,2,...,n,n,n,n,n} with the property that b(1) >= b(2) >= ... >= b(n), where five k's are skipped by b(k) for k=1..n.

%I #26 Sep 27 2023 02:47:18

%S 1,1,4,16,104,508,5136,28224,333360,2793888,34010208,276522240,

%T 5903380896,50068045536,892740867024,13555604385504,260760485969664,

%U 3084227796562768,91112167715233008,1145087508241888160

%N The number of permutations of {1,1,1,1,1,2,2,2,2,2,...,n,n,n,n,n} with the property that b(1) >= b(2) >= ... >= b(n), where five k's are skipped by b(k) for k=1..n.

%e In case of n = 1.

%e | | b(1)

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

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

%e In case of n = 2.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

%Y Column 5 of A332762.

%Y Cf. A104431, A322178, A332748, A332752, A332783, A332784.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 24 2020

%E a(10)-a(19) from _Max Alekseyev_, Sep 26 2023