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

1,1

Comments

Column 3 of A201700.

Links

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

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)

Example

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

Crossrefs

Cf. A201700.

Sequence in context: A163471 A054122 A213230 * A074566 A291076 A113328

Adjacent sequences: A201692 A201693 A201694 * A201696 A201697 A201698

Keyword

nonn

Author

R. H. Hardin, Dec 03 2011

Status

approved