A223833 Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

7, 22, 48, 89, 149, 232, 342, 483, 659, 874, 1132, 1437, 1793, 2204, 2674, 3207, 3807, 4478, 5224, 6049, 6957, 7952, 9038, 10219, 11499, 12882, 14372, 15973, 17689, 19524, 21482, 23567, 25783, 28134, 30624, 33257, 36037, 38968, 42054, 45299, 48707, 52282

Offset

1,1

Comments

Column 3 of A223838.

Links

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

Formula

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

Conjectures from Colin Barker, Aug 23 2018: (Start)

G.f.: x*(7 - 6*x + 2*x^2 + x^3) / (1 - x)^4.

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

(End)

Example

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

Crossrefs

Cf. A223838.

Sequence in context: A331229 A299283 A244243 * A014073 A288114 A369549

Adjacent sequences: A223830 A223831 A223832 * A223834 A223835 A223836

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved