A229447 Number of 4 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

12, 25, 53, 109, 212, 387, 665, 1083, 1684, 2517, 3637, 5105, 6988, 9359, 12297, 15887, 20220, 25393, 31509, 38677, 47012, 56635, 67673, 80259, 94532, 110637, 128725, 148953, 171484, 196487, 224137, 254615, 288108, 324809, 364917, 408637, 456180

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/4)*n^4 - (1/3)*n^3 + (13/4)*n^2 + (11/6)*n + 7.

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

G.f.: x*(12 - 35*x + 48*x^2 - 26*x^3 + 7*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..2....0..0..0..2....0..0..0..2....0..2..2..2....0..0..0..0
..1..1..1..0....1..1..1..0....1..1..1..0....1..0..2..2....1..1..1..1
..2..2..2..1....1..1..1..0....1..1..1..1....1..0..2..2....2..2..2..2
..2..2..2..2....2..2..2..1....2..2..2..1....2..1..0..2....2..2..2..2

Crossrefs

Row 4 of A229445.

Sequence in context: A195143 A280321 A198274 * A175523 A280391 A058848

Adjacent sequences: A229444 A229445 A229446 * A229448 A229449 A229450

Keyword

nonn

Author

R. H. Hardin, Sep 23 2013

Status

approved