A263603 Number of (1+1) X (n+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, 7, 15, 27, 55, 109, 199, 347, 595, 1005, 1671, 2751, 4507, 7357, 11971, 19439, 31531, 51105, 82779, 134031, 216967, 351169, 568315, 919667, 1488175, 2408049, 3896439, 6304707, 10201375, 16506325, 26707951, 43214531, 69922747, 113137557

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) - a(n-5) + a(n-6) for n>8.

Empirical g.f.: x*(2 + x - x^3 + 7*x^4 + 4*x^5 + 3*x^6 + 2*x^7) / ((1 - x)^2*(1 + x^2)*(1 - x - x^2)). - Colin Barker, Jan 02 2019

Example

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

Crossrefs

Row 1 of A263602.

Sequence in context: A333637 A113422 A061802 * A003452 A000148 A147672

Adjacent sequences: A263600 A263601 A263602 * A263604 A263605 A263606

Keyword

nonn

Author

R. H. Hardin, Oct 22 2015

Status

approved