A264085 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 0,1 or 2,-2.

9, 39, 169, 715, 3025, 12815, 54289, 229971, 974169, 4126647, 17480761, 74049691, 313679521, 1328767775, 5628750625, 23843770275, 101003831721, 427859097159, 1812440220361, 7677619978603, 32522920134769, 137769300517679

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 4*a(n-3) + a(n-4).

Empirical g.f.: x*(9 + 3*x + 13*x^2 + 3*x^3) / ((1 + x^2)*(1 - 4*x - x^2)). - Colin Barker, Jan 04 2019

Example

Some solutions for n=4:
..1..0..2....0..1..6....0..2..1....1..0..2....0..2..1....1..0..6....1..0..6
..3..4..5....3..5..4....4..3..5....3..5..4....4..3..5....3..4..5....4..3..5
..7..6..8....2..8..7....6..8..7....7..6.12....6..7.12....2..7..8....2..8..7
..9.10.11....9.10.11....9.10.11....9.10.11....9.10.11....9.10.11....9.11.10
.12.14.13...12.14.13...12.14.13....8.14.13....8.14.13...12.14.13...12.13.14

Crossrefs

Column 2 of A264090.

Sequence in context: A124851 A317019 A124041 * A126396 A246065 A075210

Adjacent sequences: A264082 A264083 A264084 * A264086 A264087 A264088

Keyword

nonn

Author

R. H. Hardin, Nov 03 2015

Status

approved