A224168 Number of n X 3 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

50, 684, 4739, 22988, 87878, 282372, 794220, 2010035, 4668304, 10095924, 20559019, 39765666, 73565736, 130901340, 225070360, 375375241, 609239622, 964886492, 1494683371, 2269272536, 3382617538, 4958111188, 7155904828, 10181634047

Offset: 1

Author

R. H. Hardin, Mar 31 2013

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A224173.

Formula

Empirical: a(n) = (353/181440)*n^9 + (17/560)*n^8 + (9083/30240)*n^7 + (1039/720)*n^6 + (46769/8640)*n^5 + (3863/360)*n^4 + (411149/22680)*n^3 + (14863/1260)*n^2 + (6497/1260)*n - 3.

Conjectures from Colin Barker, Aug 28 2018: (Start)

G.f.: x*(50 + 184*x + 149*x^2 + 378*x^3 - 327*x^4 + 412*x^5 - 228*x^6 + 107*x^7 - 22*x^8 + 3*x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025