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A071302 1/2 times the number of n X n 0..2 matrices M with MM' mod 3 = I, where M' is the transpose of M and I is the n X n identity matrix. 6
1, 4, 24, 576, 51840, 13063680, 9170703360 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Even though the sequence has only 7 known terms (as of the time of this note), the conjecture below is based on the work (formulas, comments, etc.) by Jianing Song for sequence A318609. - Petros Hadjicostas, Dec 18 2019

LINKS

Table of n, a(n) for n=1..7.

Jianing Song, Structure of the group SO(2,Z_n).

László Tóth, Counting solutions of quadratic congruences in several variables revisited, arXiv:1404.4214 [math.NT], 2014.

László Tóth, Counting Solutions of Quadratic Congruences in Several Variables Revisited, J. Int. Seq. 17 (2014), #14.11.6.

FORMULA

Conjecture: a(n+1) = a(n)* A318609(n+1) for n >= 1. - Petros Hadjicostas, Dec 18 2019

EXAMPLE

From Petros Hadjicostas, Dec 17 2019: (Start)

For n = 2, the 2*a(2) = 8 n X n matrices M with elements in {0, 1, 2} that satisfy MM' mod 3 = I are the following:

(a) With 1 = det(M) mod 3:

[[1,0],[0,1]];  [[0,1],[2,0]]; [[0,2],[1,0]]; [[2,0],[0,2]].

This is the abelian group SO(2, Z_3). See the comments for sequence A060968.

(b) With 2 = det(M) mod 3:

[[0,1],[1,0]];  [[0,2],[2,0]]; [[1,0],[0,2]]; [[2,0],[0,1]].

Note that, for n = 3, we have 2*a(3) = 2*24 = 48 = A264083(3). (End)

CROSSREFS

Cf. A003920, A060968, A071303, A071304, A071305, A071306, A071307, A071308, A071309, A071310, A071900, A087784, A208895, A264083, A318609.

Sequence in context: A111425 A013100 A013061 * A211215 A249028 A216092

Adjacent sequences:  A071299 A071300 A071301 * A071303 A071304 A071305

KEYWORD

nonn,more

AUTHOR

R. H. Hardin, Jun 11 2002

STATUS

approved

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Last modified June 14 21:04 EDT 2021. Contains 345039 sequences. (Running on oeis4.)