A264667 Number of optimal solutions to the maximal number of diagonals problem studied in A264041.

2, 4, 28, 108, 2, 13968, 480, 7914054, 433284, 18726123500, 256, 178290006448984, 14454384, 6631290958957860856, 1401615406696, 941558205279187913101914, 1767136, 500995759754153499284692617816, 31163356068736, 984452644453618816989710782436259368

Offset

1,1

Comments

Solutions that differ by a rotation and/or reflection are counted as different. - N. J. A. Sloane, Nov 20 2015

The paper by Boyland et al. gives a(13) = 14454384 and a(15) = 1401615406696. - Eric M. Schmidt, Aug 30 2017

Links

Table of n, a(n) for n=1..20.

Peter Boyland, Gabriella Pintér, István Laukó, Ivan Roth, Jon E. Schoenfield, and Stephen Wasielewski, On the Maximum Number of Non-intersecting Diagonals in an Array, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.4.

Example

For n=2 the 4 solutions are:
.\
\\
--
/.
//
--
\\
\.
--
//
./
--
where the dot indicates an empty cell.

Crossrefs

Cf. A264041.

Sequence in context: A259375 A192374 A274526 * A356700 A357158 A259134

Adjacent sequences: A264664 A264665 A264666 * A264668 A264669 A264670

Keyword

nonn

Author

Rob Pratt, Nov 20 2015

Extensions

a(8)-a(13) from Andrew Howroyd, Feb 03 2018

a(14)-a(20) from Andrew Howroyd, Jun 22 2018

Status

approved