A263582 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 1 or 2, and rows and columns in increasing lexicographic order.

1, 4, 18, 70, 292, 1212, 5028, 20832, 86360, 358008, 1484112, 6152272, 25503888, 105724928, 438276640, 1816850528, 7531649344, 31222019264, 129429085248, 536540828672, 2224199146368, 9220289638272, 38222180397312, 158447850514688

Offset

1,2

Comments

Column 1 of A263586.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +2*a(n-3) +4*a(n-4) -8*a(n-5).

Empirical: G.f.: -x*(-1-2*x^2+4*x^3) / ( 1-4*x-2*x^3-4*x^4+8*x^5 ). - R. J. Mathar, Nov 03 2015

Example

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

Crossrefs

Cf. A263586.

Sequence in context: A171074 A005367 A050184 * A034352 A358463 A159715

Adjacent sequences: A263579 A263580 A263581 * A263583 A263584 A263585

Keyword

nonn

Author

R. H. Hardin, Oct 22 2015

Status

approved