A071305 - OEIS

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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).

1, 8, 144, 27648, 37324800, 300987187200, 13311459341107200, 3680352278629318656000, 6233449457837263300853760000, 63077322283364184001573740871680000, 3794639489522011031097665950031114403840000, 1374795579913014967183977466315375129593674465280000

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..12.

FORMULA

a(n) = A003053(n) * A071302(n). - Max Alekseyev, Nov 06 2022

EXAMPLE

From Petros Hadjicostas, Dec 16 2019: (Start)

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:

[[0,1],[1,0]]; [[0,1],[5,0]]; [[0,5],[1,0]]; [[0,5],[5,0]];

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

[[3,2],[2,3]]; [[3,2],[4,3]]; [[3,4],[2,3]]; [[3,4],[4,3]];

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

(End)

CROSSREFS

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

Sequence in context: A024285 A111687 A231851 * A172150 A105046 A123812

Adjacent sequences: A071302 A071303 A071304 * A071306 A071307 A071308

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 11 2002

EXTENSIONS

Terms a(7) onward from Max Alekseyev, Nov 06 2022

STATUS

approved