A250846 Number of (n+1) X (1+1) 0..3 arrays with nondecreasing 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.

100, 543, 2670, 12311, 54410, 233683, 983950, 4085631, 16796370, 68555723, 278351030, 1125823351, 4540620730, 18274604163, 73435058910, 294750719471, 1182035443490, 4737241699003, 18976271027590, 75987005717991

Offset: 1

Author

R. H. Hardin, Nov 28 2014

Keywords

• nonn

Comments

Column 1 of A250853.

Examples

			Some solutions for n=4
..3..2....2..0....3..0....0..0....1..1....1..1....3..3....3..2....3..0....3..3
..0..0....0..2....0..0....0..0....0..0....0..0....1..1....0..0....0..1....3..3
..2..3....0..2....2..2....2..3....3..3....1..1....2..3....0..1....1..2....1..1
..2..3....0..3....1..1....1..2....0..0....2..3....2..3....0..1....0..1....1..1
..1..2....0..3....0..1....0..2....1..3....0..2....0..1....0..2....1..3....1..1
		

Links

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

Formula

Empirical: a(n) = 10*a(n-1) -35*a(n-2) +50*a(n-3) -24*a(n-4); a(n) = (832*4^n-846*3^n+204*2^n+2)/12.

G.f.: x*(100 - 457*x + 740*x^2 - 384*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)) (conjectured). - Colin Barker, Jan 18 2018