A213270 Costas arrays such that the corresponding permutation is an involution.

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, 14, 0, 10

Offset

1,2

Comments

Self-inverse 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 (4, 7, 9, 1, 6, 5, 2, 8, 3) is an involution and corresponds to a Costas array:
   4  7  9  1  6  5  2  8  3  (Permutation: p(1), p(2), p(3), ..., p(n) )
   3  2 -8  5 -1 -3  6 -5     (step-1 differences: p(2)-p(1), p(3)-p(2), ... )
   5 -6 -3  4 -4  3  1        (step-2 differences: p(3)-p(1), p(4)-p(2), ... )
  -3 -1 -4  1  2 -2           (step-3 differences: p(4)-p(1), p(5)-p(2), ... )
   2 -2 -7  7 -3              ( etc. )
   1 -5 -1  2
  -2  1 -6
   4 -4
  -1

Crossrefs

Cf. A008404 (Costas arrays), A213271 (Costas arrays that are derangements), A213338 (Costas arrays that are cyclic), A213339 (Costas arrays that are connected).

Sequence in context: A293177 A231382 A360314 * A307522 A130707 A131562

Adjacent sequences: A213267 A213268 A213269 * A213271 A213272 A213273

Keyword

nonn,hard,more

Author

Joerg Arndt, Jun 08 2012

Status

approved