A263598 Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 filled by rows with each element moved a city block distance of 0 or 2, and rows and columns in increasing lexicographic order.

2, 8, 24, 60, 160, 448, 1232, 3344, 9120, 24960, 68224, 186304, 508928, 1390592, 3799296, 10379520, 28357120, 77473792, 211662848, 578272256, 1579868160, 4316282880, 11792306176, 32217174016, 88018952192, 240472260608

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 4*a(n-3) + 4*a(n-4).

Empirical g.f.: 2*x*(1 + 2*x + 4*x^2 + 2*x^3) / ((1 + 2*x^2)*(1 - 2*x - 2*x^2)). - Colin Barker, Jan 02 2019

Example

Some solutions for n=4:
..0..2....0..2....0..2....0..2....0..1....0..1....0..2....0..2....0..5....0..1
..1..7....1..3....1..3....1..4....2..4....2..3....1..7....1..4....2..3....2..7
..3..5....4..6....4..5....3..5....3..6....4..5....3..9....3..9....4..1....3..9
..6..4....5..7....6..7....6..7....5..8....6..7....6..4....5..8....6..7....5..4
..8..9....8..9....8..9....8..9....7..9....8..9....8..5....7..6....8..9....8..6

Crossrefs

Column 1 of A263602.

Sequence in context: A051745 A006734 A131064 * A075218 A006728 A234933

Adjacent sequences: A263595 A263596 A263597 * A263599 A263600 A263601

Keyword

nonn

Author

R. H. Hardin, Oct 22 2015

Status

approved