%I #16 Oct 18 2019 13:30:49

%S 0,1,2,2,18,42,66,168,300,910,1882,3192,5320,7166,8346,9042,7760,6668,

%T 4620,2822,1528,942,282,92,32,22,88,256,24

%N Costas arrays such that the corresponding permutation is a derangement.

%C Fixed-point free permutations such that each row in the difference table consists of pairwise distinct elements (see example).

%H Scott Rickard, <a href="http://costasarrays.org/">costasarrays.org</a> (information and papers about Costas arrays).

%e The permutation (9, 8, 1, 6, 3, 7, 2, 4, 5) is a derangement and corresponds to a Costas array:

%e 9 8 1 6 3 7 2 4 5 (Permutation: p(1), p(2), p(3), ..., p(n) )

%e -1 -7 5 -3 4 -5 2 1 (step-1 differences: p(2)-p(1), p(3)-p(2), ... )

%e -8 -2 2 1 -1 -3 3 (step-2 differences: p(3)-p(1), p(4)-p(2), ... )

%e -3 -5 6 -4 1 -2 (step-3 differences: p(4)-p(1), p(5)-p(2), ... )

%e -6 -1 1 -2 2 ( etc. )

%e -2 -6 3 -1

%e -7 -4 4

%e -5 -3

%e -4

%Y Cf. A008404 (Costas arrays), A213270 (Costas arrays that are involutions), A213338 (Costas arrays that are cyclic), A213339 (Costas arrays that are connected).

%K nonn,hard,more

%O 1,3

%A _Joerg Arndt_, Jun 08 2012