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

1,1

Comments

Column 3 of A180985.

Links

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

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)

Example

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

Crossrefs

Cf. A180985.

Sequence in context: A356726 A208666 A125068 * A318019 A182902 A108765

Adjacent sequences: A184135 A184136 A184137 * A184139 A184140 A184141

Keyword

nonn

Author

R. H. Hardin, Jan 09 2011

Status

approved