A224185 Number of n X 3 0..2 arrays with rows unimodal and columns nondecreasing.

22, 158, 684, 2205, 5852, 13524, 28176, 54153, 97570, 166738, 272636, 429429, 655032, 971720, 1406784, 1993233, 2770542, 3785446, 5092780, 6756365, 8849940, 11458140, 14677520, 18617625, 23402106, 29169882, 36076348, 44294629, 54016880

Offset

1,1

Comments

Column 3 of A224190.

Links

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

Formula

Empirical: a(n) = (23/360)*n^6 + (27/40)*n^5 + (205/72)*n^4 + (49/8)*n^3 + (319/45)*n^2 + (21/5)*n + 1.

Conjectures from Colin Barker, Aug 29 2018: (Start)

G.f.: x*(22 + 4*x + 40*x^2 - 35*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Cf. A224190.

Sequence in context: A244868 A223913 A189416 * A185859 A173393 A141306

Adjacent sequences: A224182 A224183 A224184 * A224186 A224187 A224188

Keyword

nonn

Author

R. H. Hardin, Apr 01 2013

Status

approved