A224143 Number of n X 5 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

16, 86, 275, 691, 1509, 2985, 5471, 9431, 15457, 24285, 36811, 54107, 77437, 108273, 148311, 199487, 263993, 344293, 443139, 563587, 709013, 883129, 1089999, 1334055, 1620113, 1953389, 2339515, 2784555, 3295021, 3877889, 4540615, 5291151, 6137961

Offset

1,1

Comments

Column 5 of A224146.

Links

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

Formula

Empirical: a(n) = (2/15)*n^5 + (2/3)*n^4 + (10/3)*n^3 + (25/3)*n^2 + (203/15)*n - 17 for n>2.

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

G.f.: x*(16 - 10*x - x^2 + 11*x^3 + 8*x^4 - 10*x^5 + x^6 + x^7) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>8.

(End)

Example

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

Crossrefs

Cf. A224146.

Sequence in context: A183777 A050256 A223835 * A225007 A352953 A070052

Adjacent sequences: A224140 A224141 A224142 * A224144 A224145 A224146

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved