A209095 Number of n X 3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

5, 76, 1326, 23248, 407832, 7154944, 125526240, 2202232576, 38635976064, 677829707776, 11891846929920, 208630607073280, 3660216151873536, 64214845877125120, 1126585496573239296, 19764820171301257216

Offset

1,1

Comments

Column 3 of A209100.

Links

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

Formula

Empirical: a(n) = 20*a(n-1) - 44*a(n-2) + 16*a(n-3) for n>4.

Conjectures from Colin Barker, Jul 08 2018: (Start)

G.f.: x*(5 - 4*x)*(1 - 4*x + 2*x^2) / ((1 - 2*x)*(1 - 18*x + 8*x^2)).

a(n) = 2^(n-3) + ((9-sqrt(73))^n*(-25+sqrt(73)) + (9+sqrt(73))^n*(25+sqrt(73))) / (16*sqrt(73)) for n>1.

(End)

Example

Some solutions for n=4:
..0..0..1....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1....0..1..2
..1..2..1....1..1..1....1..1..2....2..0..0....1..1..2....1..0..2....1..2..1
..1..0..1....2..0..0....2..0..0....2..1..0....0..0..0....1..1..2....0..2..1
..2..1..2....1..2..2....1..1..1....2..2..2....1..2..0....0..0..1....1..2..2

Crossrefs

Cf. A209100.

Sequence in context: A277296 A364323 A011918 * A136300 A196689 A196725

Adjacent sequences: A209092 A209093 A209094 * A209096 A209097 A209098

Keyword

nonn

Author

R. H. Hardin, Mar 05 2012

Status

approved