A224141 Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

7, 22, 49, 92, 155, 242, 357, 504, 687, 910, 1177, 1492, 1859, 2282, 2765, 3312, 3927, 4614, 5377, 6220, 7147, 8162, 9269, 10472, 11775, 13182, 14697, 16324, 18067, 19930, 21917, 24032, 26279, 28662, 31185, 33852, 36667, 39634, 42757, 46040, 49487, 53102

Offset

1,1

Comments

Column 3 of A224146.

Links

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

Formula

Empirical: a(n) = (2/3)*n^3 + 2*n^2 + (13/3)*n.

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

G.f.: x*(7 - 6*x + 3*x^2) / (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..0..0....0..0..0....0..1..1....0..1..0....0..0..1....0..1..0....0..0..1
..0..0..0....0..0..0....1..1..1....0..1..1....0..0..1....0..1..0....1..1..1
..0..0..1....1..1..1....1..1..1....1..1..1....0..1..1....0..1..0....1..1..1

Crossrefs

Cf. A224146.

Sequence in context: A288114 A369549 A129109 * A002412 A211652 A211650

Adjacent sequences: A224138 A224139 A224140 * A224142 A224143 A224144

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved