A224168 Number of n X 3 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

50, 684, 4739, 22988, 87878, 282372, 794220, 2010035, 4668304, 10095924, 20559019, 39765666, 73565736, 130901340, 225070360, 375375241, 609239622, 964886492, 1494683371, 2269272536, 3382617538, 4958111188, 7155904828, 10181634047

Offset

1,1

Comments

Column 3 of A224173.

Links

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

Formula

Empirical: a(n) = (353/181440)*n^9 + (17/560)*n^8 + (9083/30240)*n^7 + (1039/720)*n^6 + (46769/8640)*n^5 + (3863/360)*n^4 + (411149/22680)*n^3 + (14863/1260)*n^2 + (6497/1260)*n - 3.

Conjectures from Colin Barker, Aug 28 2018: (Start)

G.f.: x*(50 + 184*x + 149*x^2 + 378*x^3 - 327*x^4 + 412*x^5 - 228*x^6 + 107*x^7 - 22*x^8 + 3*x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

Example

Some solutions for n=3:
..0..0..1....1..1..0....2..2..2....0..0..1....0..0..1....1..0..0....2..2..1
..1..2..1....2..1..0....2..2..2....1..2..1....0..0..1....2..3..2....3..3..1
..2..2..3....2..3..3....2..2..3....3..3..1....0..2..2....3..3..3....3..3..3

Crossrefs

Cf. A224173.

Sequence in context: A282766 A323485 A052460 * A223859 A223982 A128799

Adjacent sequences: A224165 A224166 A224167 * A224169 A224170 A224171

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved