A201695 Number of n X 3 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

3, 18, 116, 395, 989, 2068, 3838, 6541, 10455, 15894, 23208, 32783, 45041, 60440, 79474, 102673, 130603, 163866, 203100, 248979, 302213, 363548, 433766, 513685, 604159, 706078, 820368, 947991, 1089945, 1247264, 1421018, 1612313, 1822291

Offset: 1

Author

R. H. Hardin, Dec 03 2011

Keywords

• nonn

Comments

Column 3 of A201700.

Examples

			Some solutions for n=4:
..1..2..2....0..0..1....0..2..2....0..2..2....1..1..2....0..0..2....0..0..2
..1..2..2....0..2..0....2..0..1....1..1..2....1..2..1....0..2..0....0..1..0
..2..1..2....0..2..0....2..0..1....1..2..0....2..0..1....2..0..0....2..0..0
..2..2..0....2..0..0....2..1..0....2..0..0....2..1..0....2..0..0....2..0..0
		

Links

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

Crossrefs

Cf. A201700.

Formula

Empirical: a(n) = (3/2)*n^4 + (4/3)*n^3 - 4*n^2 - (29/6)*n + 9.

Conjectures from Colin Barker, May 23 2018: (Start)

G.f.: x*(3 + 3*x + 56*x^2 - 35*x^3 + 9*x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)