A223764 Number of n X 2 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

4, 12, 28, 56, 101, 169, 267, 403, 586, 826, 1134, 1522, 2003, 2591, 3301, 4149, 5152, 6328, 7696, 9276, 11089, 13157, 15503, 18151, 21126, 24454, 28162, 32278, 36831, 41851, 47369, 53417, 60028, 67236, 75076, 83584, 92797, 102753, 113491, 125051

Offset: 1

Author

R. H. Hardin, Mar 27 2013

Keywords

• nonn

Comments

Column 2 of A223770.

Examples

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

Links

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

Crossrefs

Cf. A223770.

Formula

Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 + (35/24)*n^2 + (5/4)*n + 1.

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

G.f.: x*(2 - 2*x + x^2)^2 / (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)