A198598 Number of 2n X 4 0..3 arrays with values 0..3 introduced in row major order and each element equal to exactly two horizontal and vertical neighbors.

1, 5, 32, 251, 1985, 15761, 125168, 994127, 7895777, 62711837, 498086240, 3956031011, 31420628321, 249557171369, 1982098563440, 15742744249463, 125036161801025, 993095073749045, 7887620760000800, 62647135102634315

Offset

1,2

Comments

Column 2 of A198604.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 9*a(n-1) -4*a(n-2) -36*a(n-3) +5*a(n-4) +27*a(n-5).

Empirical g.f.: x*(1 - 4*x - 9*x^2 + 19*x^3 + 29*x^4) / ((1 - x)*(1 + x)*(1 - 9*x + 5*x^2 + 27*x^3)). - Colin Barker, May 14 2018

Example

Some solutions for n=3:
..0..0..1..1....0..0..0..0....0..0..0..0....0..0..1..1....0..0..1..1
..0..0..1..1....0..1..1..0....0..1..1..0....0..0..1..1....0..0..1..1
..1..1..0..0....0..1..1..0....0..1..1..0....2..2..2..2....2..2..3..3
..1..1..0..0....0..0..0..0....0..0..0..0....2..0..0..2....2..2..3..3
..0..0..1..1....1..1..2..2....2..2..1..1....2..0..0..2....3..3..2..2
..0..0..1..1....1..1..2..2....2..2..1..1....2..2..2..2....3..3..2..2

Crossrefs

Cf. A198604.

Sequence in context: A127089 A241769 A208046 * A369785 A215916 A068102

Adjacent sequences: A198595 A198596 A198597 * A198599 A198600 A198601

Keyword

nonn

Author

R. H. Hardin, Oct 27 2011

Status

approved