A224033 Number of n X 3 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

4, 13, 37, 105, 298, 848, 2419, 6908, 19737, 56401, 161181, 460622, 1316360, 3761867, 10750568, 30722673, 87798365, 250907593, 717036338, 2049125344, 5855930115, 16734904820, 47824518777, 136671503209, 390575802373, 1116176041318

Offset

1,1

Comments

Column 3 of A224038.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - a(n-3) + 2*a(n-5).

Empirical g.f.: x*(1 - x)*(4 + x - 2*x^2 - 2*x^3) / (1 - 4*x + 3*x^2 + x^3 - 2*x^5). - Colin Barker, Aug 26 2018

Example

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

Crossrefs

Cf. A224038.

Sequence in context: A300985 A080145 A097551 * A095126 A077842 A091874

Adjacent sequences: A224030 A224031 A224032 * A224034 A224035 A224036

Keyword

nonn

Author

R. H. Hardin, Mar 30 2013

Status

approved