A229423 Number of n X 3 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.

8, 27, 83, 222, 524, 1116, 2187, 4005, 6936, 11465, 18219, 27992, 41772, 60770, 86451, 120567, 165192, 222759, 296099, 388482, 503660, 645912, 820091, 1031673, 1286808, 1592373, 1956027, 2386268, 2892492, 3485054, 4175331, 4975787, 5900040, 6962931

Offset: 1

Author

R. H. Hardin, Sep 22 2013

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A229428.

Formula

Empirical: a(n) = (1/360)*n^6 + (1/20)*n^5 + (5/18)*n^4 + (2/3)*n^3 + (799/360)*n^2 + (107/60)*n + 3.

Conjectures from Colin Barker, Sep 15 2018: (Start)

G.f.: x*(8 - 29*x + 62*x^2 - 72*x^3 + 48*x^4 - 18*x^5 + 3*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)