A216796 Number of permutations of an n X 4 array with each element moving exactly one horizontally or vertically and without 2-loops.

0, 6, 8, 88, 292, 1774, 7676, 39844, 186996, 927134, 4460016, 21812696, 105716132, 514912230, 2501152692, 12167375908, 59142175940, 287602784246, 1398239939960, 6798750327544, 33055539575012, 160722650037822, 781448253270316

Offset

1,2

Comments

Column 4 of A216800.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +10*a(n-2) -28*a(n-3) -7*a(n-4) +30*a(n-5) -8*a(n-6).

Empirical g.f.: 2*x^2*(1 - 2*x)*(3 - 2*x - 6*x^2 + 2*x^3) / ((1 - x)*(1 - 3*x - 13*x^2 + 15*x^3 + 22*x^4 - 8*x^5)). - Colin Barker, Feb 23 2018

Example

Some solutions for n=4:
..4..0..3..7....4..0..3..7....1..2..3..7....1..5..3..7....4..0..1..2
..5..1..2.11....5..1..2.11....0..9..5..6....0..4..2.11....8..6..7..3
.12..8..6.15....9.13..6.15....4.10.11.15....9.10..6.15...12..5.11.15
.13..9.10.14....8.12.10.14....8.12.13.14....8.12.13.14...13..9.10.14

Crossrefs

Cf. A216800.

Sequence in context: A284635 A250256 A242490 * A137127 A013241 A013237

Adjacent sequences: A216793 A216794 A216795 * A216797 A216798 A216799

Keyword

nonn

Author

R. H. Hardin, Sep 17 2012

Status

approved