A229440 Number of n X 3 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

5, 10, 22, 53, 128, 293, 625, 1244, 2327, 4124, 6976, 11335, 17786, 27071, 40115, 58054, 82265, 114398, 156410, 210601, 279652, 366665, 475205, 609344, 773707, 973520, 1214660, 1503707, 1847998, 2255683, 2735783, 3298250, 3954029, 4715122

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/360)*n^6 + (1/120)*n^5 + (1/36)*n^4 + (5/24)*n^3 - (11/360)*n^2 + (167/60)*n + 2.

Conjectures from Colin Barker, Sep 17 2018: (Start)

G.f.: x*(5 - 25*x + 57*x^2 - 66*x^3 + 44*x^4 - 15*x^5 + 2*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:
..0..2..2....0..2..2....0..2..2....0..2..2....0..2..2....0..2..2....0..2..2
..1..0..2....0..2..2....1..0..2....0..2..2....0..2..2....1..0..0....1..0..2
..1..0..2....1..0..2....1..0..2....1..0..2....0..2..2....1..1..1....1..1..0
..1..0..2....2..1..0....1..1..0....1..1..0....1..0..2....2..2..2....1..1..0

Crossrefs

Column 3 of A229445.

Sequence in context: A087746 A064694 A264147 * A067622 A362284 A196240

Adjacent sequences: A229437 A229438 A229439 * A229441 A229442 A229443

Keyword

nonn

Author

R. H. Hardin, Sep 23 2013

Status

approved