A250578 Number of (n+1) X (3+1) 0..1 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.

55, 142, 336, 778, 1779, 4077, 9346, 21510, 49579, 114548, 264881, 613191, 1420035, 3290061, 7623702, 17668834, 40951324, 94920278, 220016344, 509991358, 1182147415, 2740217734, 6351824316, 14723589157, 34129405898, 79112386680

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 6*a(n-2) - 7*a(n-3) + 21*a(n-4) - 14*a(n-5) - a(n-6) + 4*a(n-7) - a(n-8).

Empirical g.f.: x*(55 - 133*x - 44*x^2 + 335*x^3 - 256*x^4 - 10*x^5 + 68*x^6 - 17*x^7) / ((1 - x)^3*(1 - 2*x - 3*x^2 + 5*x^3 + x^4 - x^5)). - Colin Barker, Nov 15 2018

Example

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

Crossrefs

Column 3 of A250583.

Sequence in context: A218161 A044306 A044687 * A130745 A096664 A067978

Adjacent sequences: A250575 A250576 A250577 * A250579 A250580 A250581

Keyword

nonn

Author

R. H. Hardin, Nov 25 2014

Status

approved