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%I #14 Jun 09 2012 04:54:55
%S 1,2,2,2,4,10,20,18,20,28,36,34,50,46,62,40,38,20,12,8,16,10,20,0,4,4,
%T 14,0,10
%N Costas arrays such that the corresponding permutation is an involution.
%C Self-inverse 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 (4, 7, 9, 1, 6, 5, 2, 8, 3) is an involution and corresponds to a Costas array:
%e 4 7 9 1 6 5 2 8 3 (Permutation: p(1), p(2), p(3), ..., p(n) )
%e 3 2 -8 5 -1 -3 6 -5 (step-1 differences: p(2)-p(1), p(3)-p(2), ... )
%e 5 -6 -3 4 -4 3 1 (step-2 differences: p(3)-p(1), p(4)-p(2), ... )
%e -3 -1 -4 1 2 -2 (step-3 differences: p(4)-p(1), p(5)-p(2), ... )
%e 2 -2 -7 7 -3 ( etc. )
%e 1 -5 -1 2
%e -2 1 -6
%e 4 -4
%e -1
%Y Cf. A008404 (Costas arrays), A213271 (Costas arrays that are derangements), A213338 (Costas arrays that are cyclic), A213339 (Costas arrays that are connected).
%K nonn,hard,more
%O 1,2
%A _Joerg Arndt_, Jun 08 2012
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