A196294 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

3, 9, 20, 61, 187, 536, 1597, 4849, 14582, 44097, 134349, 409428, 1249517, 3822519, 11705002, 35866253, 109991817, 337493970, 1035913925, 3180693901, 9768462112, 30005758115, 92181317503, 283222651372, 870256732085, 2674196289015

Offset: 1

Author

R. H. Hardin, Sep 30 2011

Keywords

• nonn

Comments

Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 4's, every 4 is next to 4 2's.

Column 2 of A196300.

Examples

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

Links

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

Crossrefs

Cf. A196300.

Formula

Empirical: a(n) = 2*a(n-1) +4*a(n-2) +6*a(n-3) -9*a(n-4) -38*a(n-5) -32*a(n-6) -11*a(n-7) +6*a(n-8) +a(n-9).

Empirical g.f.: x*(1 + x)^2*(3 - 3*x - 7*x^2 - 16*x^3 - 3*x^4 + 15*x^5 + 2*x^6) / ((1 - x - 7*x^3 - x^4)*(1 - x - 5*x^2 - 4*x^3 - x^4 + x^5)). - Colin Barker, May 08 2018