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

1,1

Links

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

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)

Example

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

Crossrefs

Column 3 of A229428.

Sequence in context: A276920 A193006 A212745 * A166867 A343323 A079712

Adjacent sequences: A229420 A229421 A229422 * A229424 A229425 A229426

Keyword

nonn

Author

R. H. Hardin, Sep 22 2013

Status

approved