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A213271
Costas arrays such that the corresponding permutation is a derangement.
4
0, 1, 2, 2, 18, 42, 66, 168, 300, 910, 1882, 3192, 5320, 7166, 8346, 9042, 7760, 6668, 4620, 2822, 1528, 942, 282, 92, 32, 22, 88, 256, 24
OFFSET
1,3
COMMENTS
Fixed-point free permutations such that each row in the difference table consists of pairwise distinct elements (see example).
LINKS
Scott Rickard, costasarrays.org (information and papers about Costas arrays).
EXAMPLE
The permutation (9, 8, 1, 6, 3, 7, 2, 4, 5) is a derangement and corresponds to a Costas array:
9 8 1 6 3 7 2 4 5 (Permutation: p(1), p(2), p(3), ..., p(n) )
-1 -7 5 -3 4 -5 2 1 (step-1 differences: p(2)-p(1), p(3)-p(2), ... )
-8 -2 2 1 -1 -3 3 (step-2 differences: p(3)-p(1), p(4)-p(2), ... )
-3 -5 6 -4 1 -2 (step-3 differences: p(4)-p(1), p(5)-p(2), ... )
-6 -1 1 -2 2 ( etc. )
-2 -6 3 -1
-7 -4 4
-5 -3
-4
CROSSREFS
Cf. A008404 (Costas arrays), A213270 (Costas arrays that are involutions), A213338 (Costas arrays that are cyclic), A213339 (Costas arrays that are connected).
Sequence in context: A168296 A205454 A100304 * A096190 A136434 A121670
KEYWORD
nonn,hard,more
AUTHOR
Joerg Arndt, Jun 08 2012
STATUS
approved