A203366 Number of n X 3 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by both a 1 and a 0.

3, 30, 206, 1570, 11541, 85932, 636912, 4728287, 35081894, 260344178, 1931891935, 14336007171, 106382441959, 789428803920, 5858083254752, 43470863287881, 322582598884187, 2393776652484473, 17763408799398613, 131816263437678307

Offset

1,1

Comments

Column 3 of A203371.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +26*a(n-2) +44*a(n-3) +45*a(n-4) +24*a(n-5) -a(n-6) -17*a(n-7) +2*a(n-8) -2*a(n-9).

Empirical g.f.: x*(3 + 21*x + 38*x^2 + 40*x^3 + 20*x^4 + 3*x^5 - 17*x^6 + 2*x^7 - 2*x^8) / (1 - 3*x - 26*x^2 - 44*x^3 - 45*x^4 - 24*x^5 + x^6 + 17*x^7 - 2*x^8 + 2*x^9). - Colin Barker, Jun 04 2018

Example

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

Crossrefs

Cf. A203371.

Sequence in context: A032263 A003771 A121100 * A130546 A051133 A332426

Adjacent sequences: A203363 A203364 A203365 * A203367 A203368 A203369

Keyword

nonn

Author

R. H. Hardin, Dec 31 2011

Status

approved