A229422 Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.

5, 12, 27, 55, 102, 175, 282, 432, 635, 902, 1245, 1677, 2212, 2865, 3652, 4590, 5697, 6992, 8495, 10227, 12210, 14467, 17022, 19900, 23127, 26730, 30737, 35177, 40080, 45477, 51400, 57882, 64957, 72660, 81027, 90095, 99902, 110487, 121890, 134152

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (25/12)*n + 2.

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

G.f.: x*(5 - 13*x + 17*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..0....0..0....1..0....0..0....1..1....1..0....0..0....0..0....2..2....0..0
..0..0....1..0....1..0....0..0....2..1....2..1....0..0....1..1....2..2....1..1
..1..1....1..1....1..1....0..0....2..1....2..1....1..0....1..1....2..2....2..2
..2..2....2..1....2..1....1..1....2..2....2..1....1..0....2..1....2..2....2..2

Crossrefs

Column 2 of A229428.

Sequence in context: A078517 A170828 A357417 * A128439 A240187 A172426

Adjacent sequences: A229419 A229420 A229421 * A229423 A229424 A229425

Keyword

nonn

Author

R. H. Hardin, Sep 22 2013

Status

approved