A224134 Number of 3 X n 0..1 arrays with rows nondecreasing and antidiagonals unimodal.

8, 27, 58, 106, 175, 269, 392, 548, 741, 975, 1254, 1582, 1963, 2401, 2900, 3464, 4097, 4803, 5586, 6450, 7399, 8437, 9568, 10796, 12125, 13559, 15102, 16758, 18531, 20425, 22444, 24592, 26873, 29291, 31850, 34554, 37407, 40413, 43576, 46900, 50389, 54047

Offset

1,1

Comments

Row 3 of A224133.

Links

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

Formula

Empirical: a(n) = (2/3)*n^3 + (5/2)*n^2 + (35/6)*n for n>1.

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

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

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

(End)

Example

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

Crossrefs

Cf. A224133.

Sequence in context: A339897 A131620 A141227 * A213488 A151675 A211641

Adjacent sequences: A224131 A224132 A224133 * A224135 A224136 A224137

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved