A213271 - OEIS

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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

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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