A216797 Number of permutations of an n X 5 array with each element moving exactly one horizontally or vertically and without 2-loops.

0, 10, 0, 292, 0, 10140, 0, 361200, 0, 12911864, 0, 461788640, 0, 16516859104, 0, 590766585904, 0, 21130267285488, 0, 755777826856944, 0, 27032319708816080, 0, 966879797484085808, 0, 34582919761038885136, 0, 1236946249622251150000, 0

Offset: 1

Author

R. H. Hardin, Sep 17 2012

Keywords

• nonn

Comments

Column 5 of A216800.

Examples

			Some solutions for n=4:
..1..2..7..8..3....5..0..1..4..9....5..0..3..4..9....1..6..7..2..3
..0..5..6..9..4...10..7..2..3.14....6..1..2.13..8....0..5..8..9..4
.11.12.13.14.19...15..6.13..8.19...11.12..7.14.19...15.10.11.14.19
.10.15.16.17.18...16.11.12.17.18...10.15.16.17.18...16.17.12.13.18
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A216800.

Formula

Empirical: a(n) = 49*a(n-2) - 524*a(n-4) + 1862*a(n-6) - 1728*a(n-8).

Empirical g.f.: 2*x^2*(5 - 99*x^2 + 536*x^4 - 636*x^6) / (1 - 49*x^2 + 524*x^4 - 1862*x^6 + 1728*x^8). - Colin Barker, Mar 09 2018