A203454 Number of n X 2 0..2 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

1, 3, 9, 22, 63, 209, 686, 2228, 7365, 24619, 82433, 276500, 929936, 3133114, 10566260, 35661359, 120433051, 406897030, 1375168827, 4648638160, 15716950105, 53145110566, 179719928744, 607794550141, 2055594816788, 6952369432018

Offset

1,2

Comments

Column 2 of A203460.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -12*a(n-2) +19*a(n-3) -32*a(n-4) +15*a(n-5) -13*a(n-6) +13*a(n-7) +10*a(n-8) +7*a(n-9) +5*a(n-10) +a(n-11).

Empirical g.f.: x*(1 - 3*x + 3*x^2 - 15*x^3 + 14*x^4 + 5*x^5 + 26*x^6 + 18*x^7 + 12*x^8 + 6*x^9 + x^10) / (1 - 6*x + 12*x^2 - 19*x^3 + 32*x^4 - 15*x^5 + 13*x^6 - 13*x^7 - 10*x^8 - 7*x^9 - 5*x^10 - x^11). - Colin Barker, Jun 04 2018

Example

Some solutions for n=5:
..0..0....1..1....2..2....1..1....2..2....2..2....1..1....0..0....0..0....1..1
..0..0....1..1....2..2....2..2....2..2....2..2....1..1....0..0....2..2....1..1
..1..1....0..0....0..0....2..2....0..2....2..2....2..2....1..1....2..2....2..2
..2..2....2..2....0..0....0..0....2..2....1..1....2..2....1..1....0..0....2..2
..2..2....2..2....0..0....0..0....2..2....0..0....1..1....0..0....0..0....1..1

Crossrefs

Cf. A203460.

Sequence in context: A032284 A329163 A296582 * A197666 A146009 A326007

Adjacent sequences: A203451 A203452 A203453 * A203455 A203456 A203457

Keyword

nonn

Author

R. H. Hardin, Jan 02 2012

Status

approved