A264514 Number of (2n) X (2+1) arrays of permutations of 0..n*6-1 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

1, 3, 12, 46, 177, 684, 2640, 10180, 39249, 151326, 583444, 2249491, 8673001, 33439105, 128925825, 497078745, 1916507251, 7389171396, 28489249854, 109841457681, 423498192724, 1632814449360, 6295382298780, 24272101648369

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n = 1..105

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 13*a(n-3) - 11*a(n-4) + 6*a(n-5) - a(n-6).

Empirical g.f.: x*(1 - 3*x + 5*x^2 - 6*x^3 + 5*x^4 - x^5) / (1 - 6*x + 11*x^2 - 13*x^3 + 11*x^4 - 6*x^5 + x^6). - Colin Barker, Jan 08 2019

Example

Some solutions for n=3:
..5..4..0....3..4..0....3..4..5....3..4..0....5..4..0....3..4..5....3..4..0
..8..1..2....8..1..2....0..1..2....6..1..2....8..1..2....0..1..2....8..1..2
..3.10..6...11.10..5....9.10.11....9.10..5....3.10.11....9.10..6....9.10..5
.14..7..9....6..7.14....6..7..8...14..7..8....6..7.14...14..7..8....6..7.14
.17.16.11....9.16.17...15.16.17...17.16.11....9.16.17...17.16.11...17.16.11
.12.13.15...12.13.15...12.13.14...12.13.15...12.13.15...12.13.15...12.13.15

Crossrefs

Column 2 of A264520 (nonzero terms only).

Sequence in context: A047013 A370478 A108368 * A344684 A216946 A303191

Adjacent sequences: A264511 A264512 A264513 * A264515 A264516 A264517

Keyword

nonn

Author

R. H. Hardin, Nov 16 2015

Status

approved