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A290279 Number of permutations of [n] with a unique pair of orthogonal (diagonal, antidiagonal) X-rays.

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%I A290279 #12 Mar 31 2018 16:58:53
%S A290279 1,1,2,6,22,110,628,4396,34496,309230,3069808
%N A290279 Number of permutations of [n] with a unique pair of orthogonal (diagonal, antidiagonal) X-rays.
%C A290279 The X-rays of a permutation are sequences of (diagonal, antidiagonal) sums of the corresponding permutation matrix.
%C A290279 A unique pair of orthogonal (diagonal, antidiagonal) X-rays allows identification of the permutation.
%H A290279 C. Bebeacua, T. Mansour, A. Postnikov and S. Severini, <a href="https://arxiv.org/abs/math/0506334">On the X-rays of permutations</a>, arXiv:math/0506334 [math.CO], 2005.
%H A290279 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%H A290279 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_matrix">Permutation matrix</a>
%e A290279 a(4) = 22.  All permutations of {1,2,3,4} have unique pairs of orthogonal X-rays except 2413 and 3142, which share the same pair (0110110, 0110110):
%e A290279 .
%e A290279 .  0110110       .  0110110
%e A290279 .   \\\+--\-+    .   \\\+--\-+
%e A290279 .  2 \\| 1  |    .  3 \\|  1 |
%e A290279 .  4  \|   1|    .  1  \|1   |
%e A290279 .  1  /|1   |    .  4  /|   1|
%e A290279 .  3 //|  1 |    .  2 //| 1  |
%e A290279 .   ///+--/-+    .   ///+--/-+
%e A290279 .  0110110       .  0110110
%Y A290279 Cf. A289971, A290280.
%K A290279 nonn,more
%O A290279 0,3
%A A290279 _Alois P. Heinz_, Jul 25 2017