A224141 Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

7, 22, 49, 92, 155, 242, 357, 504, 687, 910, 1177, 1492, 1859, 2282, 2765, 3312, 3927, 4614, 5377, 6220, 7147, 8162, 9269, 10472, 11775, 13182, 14697, 16324, 18067, 19930, 21917, 24032, 26279, 28662, 31185, 33852, 36667, 39634, 42757, 46040, 49487, 53102

Offset: 1

Author

R. H. Hardin, Mar 31 2013

Keywords

• nonn

Comments

Column 3 of A224146.

Examples

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

Links

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

Crossrefs

Cf. A224146.

Formula

Empirical: a(n) = (2/3)*n^3 + 2*n^2 + (13/3)*n.

Conjectures from Colin Barker, Aug 27 2018: (Start)

G.f.: x*(7 - 6*x + 3*x^2) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)