A213271 Costas arrays such that the corresponding permutation is a derangement.

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

Table of n, a(n) for n=1..29.

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

Adjacent sequences: A213268 A213269 A213270 * A213272 A213273 A213274

Keyword

nonn,hard,more

Author

Joerg Arndt, Jun 08 2012

Status

approved