A250585 Number of (n+1) X (1+1) 0..2 arrays with nondecreasing max(x(i,j),x(i,j-1)) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

40, 167, 639, 2375, 8625, 30952, 110187, 390391, 1378890, 4860979, 17115235, 60214730, 211741401, 744338632, 2616055529, 9193203944, 32303585679, 113504084395, 398802149195, 1401180399346, 4922940442496, 17296221980468

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 7*a(n-2) - 12*a(n-3) + 21*a(n-4) + 3*a(n-5) - 15*a(n-6) + 3*a(n-7) + 3*a(n-8) - a(n-9).

Empirical g.f.: x*(40 - 73*x - 83*x^2 + 190*x^3 + 12*x^4 - 132*x^5 + 30*x^6 + 26*x^7 - 9*x^8) / ((1 - x)*(1 - 2*x - x^2 + x^3)*(1 - 3*x - 3*x^2 + 4*x^3 + x^4 - x^5)). - Colin Barker, Nov 15 2018

Example

Some solutions for n=6:
..0..0....1..1....1..1....1..1....1..2....1..1....0..2....1..1....1..2....1..0
..2..1....0..1....0..2....0..1....2..1....0..1....1..2....0..2....2..2....0..1
..1..2....1..1....2..2....0..1....1..2....0..2....0..2....1..2....0..2....0..1
..0..2....2..1....0..2....1..2....2..1....1..2....0..2....2..1....0..2....1..0
..2..2....1..2....2..1....2..1....0..2....2..2....1..2....1..2....2..1....0..1
..2..2....0..2....1..2....0..2....2..2....0..2....2..2....1..2....0..2....1..1
..1..2....2..0....0..2....2..2....0..2....2..0....0..2....2..1....2..1....1..1

Crossrefs

Column 1 of A250592.

Sequence in context: A146762 A190073 A250592 * A260169 A205249 A211155

Adjacent sequences: A250582 A250583 A250584 * A250586 A250587 A250588

Keyword

nonn

Author

R. H. Hardin, Nov 25 2014

Status

approved