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 A071306 1/2 times the number of n X n 0..6 matrices M with MM' mod 7 = I, where M' is the transpose of M and I is the n X n identity matrix. 6
 1, 8, 336, 112896, 276595200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Even though only 5 terms are known for this sequence, my conjecture below is based on the work (comments, formulas, etc.) of Jianing Song for sequence A318609. - Petros Hadjicostas, Dec 19 2019 LINKS FORMULA Conjecture: Let b(n) be the number of solutions to the equation Sum_{i = 1..n} x_i^2 = 1 (mod 7) with x_i in 0..6. We conjecture that b(n) = 7*b(n-1) - 7*b(n-2) + 49*b(n-3) for n >= 4 with b(1) = 2, b(2) = 8, and b(3) = 42. We also conjecture that a(n+1) = a(n)*b(n+1) for n >= 1. - Petros Hadjicostas, Dec 19 2019 EXAMPLE From Petros Hadjicostas, Dec 19 2019: (Start) For n = 2, the 2*a(2) = 16 n X n matrices M with elements in 0..6 that satisfy MM' = I are the following: (a) those with 1 = det(M) mod 7: [[1,0],[0,1]]; [[0,1],[6,0]]; [[0,6],[1,0]]; [[2,2],[5,2]]; [[2,5],[2,2]]; [[5,2],[5,5]]; [[5,5],[2,5]]; [[6,0],[0,6]]. These are the elements of the abelian group SO(2,Z_7). See the comments for sequence A060968. (b) those with 6 = det(M) mod 7: [[0,1],[1,0]]; [[0,6],[6,0]]; [[1,0],[0,6]]; [[2,2],[2,5]]; [[2,5],[5,5]]; [[5,2],[2,2]]; [[5,5],[5,2]]; [[6,0],[0,1]]. Note that, for n = 3, we have 2*a(3) = 2*336 = 672 = A264083(7). (End) CROSSREFS Cf. A060968, A071302, A071303, A071305, A071306, A071307, A071308, A071309, A071310, A071900, A087784, A208895, A264083, A318609. Sequence in context: A285370 A247730 A258745 * A214511 A117082 A061458 Adjacent sequences:  A071303 A071304 A071305 * A071307 A071308 A071309 KEYWORD nonn,more AUTHOR R. H. Hardin, Jun 11 2002 STATUS approved

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Last modified May 9 20:59 EDT 2021. Contains 343746 sequences. (Running on oeis4.)