A264544 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

1, 2, 5, 10, 21, 44, 93, 196, 413, 870, 1833, 3862, 8137, 17144, 36121, 76104, 160345, 337834, 711789, 1499682, 3159709, 6657252, 14026293, 29552268, 62264245, 131185742, 276397777, 582347822, 1226959889, 2585105520, 5446608817

Offset

1,2

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + a(n-4).

Empirical g.f.: x*(1 + x^2) / (1 - 2*x - x^4). - Colin Barker, Jan 08 2019

Example

Some solutions for n=4:
..1..2..4....1..2..3....1..2..4....1..2..4....1..3..4....1..2..4....1..3..4
..0..6..7....0..5..6....0..5..7....0..6..7....0..5..2....0..5..7....0..6..2
..3..8..5....7..4..9....3..9.10....3..9..5....7..8.10....3..8.10....7..8..5
.10.12.13...10.12..8....6.12..8...10.12..8....6.12.13....6.12.13...10.12.13
..9.14.11...13.14.11...13.14.11...13.14.11....9.14.11....9.14.11....9.14.11

Crossrefs

Column 2 of A264550.

Sequence in context: A114279 A101400 A131403 * A052540 A018106 A247594

Adjacent sequences: A264541 A264542 A264543 * A264545 A264546 A264547

Keyword

nonn

Author

R. H. Hardin, Nov 17 2015

Status

approved