A229439 Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

4, 7, 13, 25, 47, 84, 142, 228, 350, 517, 739, 1027, 1393, 1850, 2412, 3094, 3912, 4883, 6025, 7357, 8899, 10672, 12698, 15000, 17602, 20529, 23807, 27463, 31525, 36022, 40984, 46442, 52428, 58975, 66117, 73889, 82327, 91468, 101350, 112012, 123494

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 - (1/24)*n^2 + (23/12)*n + 2.

Conjectures from Colin Barker, Sep 16 2018: (Start)

G.f.: x*(4 - 13*x + 18*x^2 - 10*x^3 + 2*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:
..0..2....0..2....0..2....1..1....0..2....0..2....0..2....0..0....0..2....0..2
..0..2....0..2....1..0....1..1....1..0....0..2....0..2....1..1....1..0....0..2
..0..2....0..2....2..1....1..1....1..0....1..0....1..0....2..2....2..1....1..0
..0..2....1..0....2..1....1..1....1..1....1..1....1..0....2..2....2..2....2..1

Crossrefs

Column 2 of A229445.

Sequence in context: A039694 A341843 A248098 * A000288 A074863 A118334

Adjacent sequences: A229436 A229437 A229438 * A229440 A229441 A229442

Keyword

nonn

Author

R. H. Hardin, Sep 23 2013

Status

approved