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a(n) = (1/2) * (number of n X n 0..5 matrices M with MM' mod 6 = I, where M' is the transpose of M and I is the n X n identity matrix).
8

%I #19 Nov 07 2022 02:28:22

%S 1,8,144,27648,37324800,300987187200,13311459341107200,

%T 3680352278629318656000,6233449457837263300853760000,

%U 63077322283364184001573740871680000,3794639489522011031097665950031114403840000,1374795579913014967183977466315375129593674465280000

%N a(n) = (1/2) * (number of n X n 0..5 matrices M with MM' mod 6 = I, where M' is the transpose of M and I is the n X n identity matrix).

%F a(n) = A003053(n) * A071302(n). - _Max Alekseyev_, Nov 06 2022

%e From _Petros Hadjicostas_, Dec 16 2019: (Start)

%e For n = 2, here are the 2*a(2) = 16 2 X 2 matrices M with elements in {0,1,2,3,4,5} that satisfy MM' mod 6 = I:

%e [[0,1],[1,0]]; [[0,1],[5,0]]; [[0,5],[1,0]]; [[0,5],[5,0]];

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

%e [[3,2],[2,3]]; [[3,2],[4,3]]; [[3,4],[2,3]]; [[3,4],[4,3]];

%e [[4,3],[3,2]]; [[4,3],[3,4]]; [[5,0],[0,1]]; [[5,0],[0,5]].

%e (End)

%Y Cf. A003053, A071302, A071303, A071304, A071306, A071307, A071308, A071309, A071310.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jun 11 2002

%E Terms a(7) onward from _Max Alekseyev_, Nov 06 2022