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

0,6

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.

Formula

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

Example

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

Crossrefs

Column k=4 of A293157.

Sequence in context: A125477 A016261 A016309 * A016259 A271029 A047795

Adjacent sequences: A190821 A190822 A190823 * A190825 A190826 A190827

Keyword

nonn

Author

R. H. Hardin, May 21 2011

Extensions

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

Status

approved