A184138 Number of n X 3 binary arrays with rows and columns in nondecreasing order.

4, 14, 45, 130, 336, 785, 1682, 3351, 6280, 11176, 19031, 31200, 49492, 76275, 114596, 168317, 242268, 342418, 476065, 652046, 880968, 1175461, 1550454, 2023475, 2614976, 3348684, 4251979, 5356300, 6697580, 8316711, 10260040, 12579897

Offset: 1

Author

R. H. Hardin, Jan 09 2011

Keywords

• nonn

Comments

Column 3 of A180985.

Examples

			Some solutions for 5 X 3:
..0..0..0....0..0..0....0..0..0....0..0..1....0..1..1....0..0..0....0..0..0
..0..0..1....0..0..1....0..0..0....0..1..0....0..1..1....0..1..1....0..0..1
..1..1..0....1..1..1....0..0..0....0..1..0....1..0..1....0..1..1....0..1..1
..1..1..0....1..1..1....0..0..1....0..1..1....1..0..1....0..1..1....1..1..0
..1..1..0....1..1..1....1..1..1....1..0..1....1..1..1....0..1..1....1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A180985.

Formula

Empirical: a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) (=polynomial degree 7).

Conjectures from Colin Barker, Apr 12 2018: (Start)

G.f.: x*(4 - 18*x + 45*x^2 - 62*x^3 + 52*x^4 - 27*x^5 + 8*x^6 - x^7) / (1 - x)^8.

a(n) = (5040 + 7860*n + 4494*n^2 + 2044*n^3 + 525*n^4 + 175*n^5 + 21*n^6 + n^7) / 5040.

(End)