A263587 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 1 or 2, and rows and columns in increasing lexicographic order.

1, 6, 12, 31, 89, 230, 536, 1171, 2439, 4882, 9470, 17935, 33331, 60994, 110208, 197059, 349285, 614522, 1074316, 1867855, 3232059, 5569206, 9560842, 16359331, 27909479, 47487870, 80606196, 136522471, 230766449, 389355662, 655827200

Offset

1,2

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) - 2*a(n-5) + 3*a(n-6) - a(n-8) for n>9.

Empirical g.f.: x*(1 + 2*x - 7*x^2 + 11*x^3 + 13*x^4 + 7*x^5 + 8*x^6 + 5*x^7 + 2*x^8) / ((1 - x)^2*(1 + x^2)*(1 - x - x^2)^2). - Colin Barker, Jan 02 2019

Example

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

Crossrefs

Row 1 of A263586.

Sequence in context: A152522 A096356 A065992 * A085611 A122608 A268283

Adjacent sequences: A263584 A263585 A263586 * A263588 A263589 A263590

Keyword

nonn

Author

R. H. Hardin, Oct 22 2015

Status

approved