cp's OEIS Frontend

A071305 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).

%I A071305 #19 Nov 07 2022 02:28:22
%S A071305 1,8,144,27648,37324800,300987187200,13311459341107200,
%T A071305 3680352278629318656000,6233449457837263300853760000,
%U A071305 63077322283364184001573740871680000,3794639489522011031097665950031114403840000,1374795579913014967183977466315375129593674465280000
%N A071305 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 A071305 a(n) = A003053(n) * A071302(n). - _Max Alekseyev_, Nov 06 2022
%e A071305 From _Petros Hadjicostas_, Dec 16 2019: (Start)
%e A071305 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 A071305 [[0,1],[1,0]]; [[0,1],[5,0]]; [[0,5],[1,0]]; [[0,5],[5,0]];
%e A071305 [[1,0],[0,1]]; [[1,0],[0,5]]; [[2,3],[3,2]]; [[2,3],[3,4]];
%e A071305 [[3,2],[2,3]]; [[3,2],[4,3]]; [[3,4],[2,3]]; [[3,4],[4,3]];
%e A071305 [[4,3],[3,2]]; [[4,3],[3,4]]; [[5,0],[0,1]]; [[5,0],[0,5]].
%e A071305 (End)
%Y A071305 Cf. A003053, A071302, A071303, A071304, A071306, A071307, A071308, A071309, A071310.
%K A071305 nonn
%O A071305 1,2
%A A071305 _R. H. Hardin_, Jun 11 2002
%E A071305 Terms a(7) onward from _Max Alekseyev_, Nov 06 2022