A196132 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,3,4 for x=0,1,2,3,4.

0, 4, 3, 8, 14, 19, 46, 56, 133, 184, 372, 599, 1064, 1874, 3147, 5692, 9516, 17053, 28980, 51004, 88089, 153086, 266660, 461205, 804810, 1392380, 2426083, 4205680, 7313450, 12699273, 22056242, 38328650, 66544359, 115648570, 200804584

Offset: 1

Author

R. H. Hardin, Sep 28 2011

Keywords

• nonn

Comments

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

Column 2 of A196138.

Examples

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

Links

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

Crossrefs

Cf. A196138.

Formula

Empirical: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) -3*a(n-5) -a(n-6) +4*a(n-7) -2*a(n-9).

Empirical g.f.: x^2*(4 + 3*x - 4*x^2 - 3*x^3 - 3*x^4 + 6*x^5 - 4*x^7) / ((1 - x)*(1 + x - 2*x^2 - 4*x^3 - 2*x^4 + x^5 + 2*x^6 - 2*x^7 - 2*x^8)). - Colin Barker, May 08 2018