A250813 Number of (1+1) X (n+1) 0..2 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.

36, 100, 225, 441, 784, 1296, 2025, 3025, 4356, 6084, 8281, 11025, 14400, 18496, 23409, 29241, 36100, 44100, 53361, 64009, 76176, 90000, 105625, 123201, 142884, 164836, 189225, 216225, 246016, 278784, 314721, 354025, 396900, 443556, 494209

Offset: 1

Author

R. H. Hardin, Nov 27 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 1 of A250812.

Formula

Empirical: a(n) = (1/4)*n^4 + (5/2)*n^3 + (37/4)*n^2 + 15*n + 9.

Conjectures from Colin Barker, Nov 21 2018: (Start)

G.f.: x*(36 - 80*x + 85*x^2 - 44*x^3 + 9*x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)