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

Author

Joerg Arndt, Jun 08 2012

Keywords

• nonn
• hard
• more

Comments

Self-inverse permutations such that each row in the difference table consists of pairwise distinct elements (see example).

Examples

			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
		

Links

• Scott Rickard, costasarrays.org (information and papers about Costas arrays).

Crossrefs

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