A224410 Number of 3 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

8, 36, 100, 228, 465, 879, 1568, 2668, 4362, 6890, 10560, 15760, 22971, 32781, 45900, 63176, 85612, 114384, 150860, 196620, 253477, 323499, 409032, 512724, 637550, 786838, 964296, 1174040, 1420623, 1709065, 2044884, 2434128, 2883408, 3399932

Offset: 1

Author

R. H. Hardin, Apr 05 2013

Keywords

• nonn

Comments

Row 3 of A224409.

Examples

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

Links

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

Crossrefs

Cf. A224409.

Formula

Empirical: a(n) = (1/720)*n^6 + (1/48)*n^5 + (29/144)*n^4 + (13/16)*n^3 + (2087/360)*n^2 + (7/6)*n.

Conjectures from Colin Barker, Aug 30 2018: (Start)

G.f.: x*(8 - 20*x + 16*x^2 + 4*x^3 - 11*x^4 + 4*x^5) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)