A190824 Number of permutations of 2 copies of 1..n introduced in order 1..n with no element equal to another within a distance of 3.

1, 0, 0, 0, 1, 20, 292, 4317, 69862, 1251584, 24728326, 535333713, 12616277612, 321762301156, 8833356675295, 259803215904436, 8151872288855008, 271848098526643604, 9602477503845334715, 358185069617609239664, 14070369448248794118128, 580623906507508489287367

Offset: 0

Author

R. H. Hardin, May 21 2011

Keywords

• nonn

Examples

			Some solutions for n=5
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..2....2....2....2....2....2....2....2....2....2....2....2....2....2....2....2
..3....3....3....3....3....3....3....3....3....3....3....3....3....3....3....3
..4....4....4....4....4....4....4....4....4....4....4....4....4....4....4....4
..5....5....5....1....5....5....1....5....5....5....5....5....1....5....5....5
..2....1....2....5....1....1....5....1....1....1....2....2....5....1....2....2
..3....3....3....3....3....2....2....2....3....2....3....3....2....3....1....1
..4....4....1....4....4....3....4....4....2....3....1....4....3....2....3....3
..1....5....5....2....2....4....3....3....5....5....4....5....4....4....4....5
..5....2....4....5....5....5....5....5....4....4....5....1....5....5....5....4
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..404
• Vaclav Kotesovec, Recurrence (of order 12)
• Everett Sullivan, Linear chord diagrams with long chords, arXiv preprint arXiv:1611.02771 [math.CO], 2016.

Crossrefs

Column k=4 of A293157.

Formula

a(n) ~ 2^(n + 1/2) * n^n / exp(n+3). - Vaclav Kotesovec, Oct 26 2017

Extensions

a(0)=1 prepended and a(15)-a(21) added by Alois P. Heinz, Oct 17 2017