A196850 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,1,0,2,4 for x=0,1,2,3,4.

2, 11, 38, 136, 496, 1792, 6440, 23306, 84180, 303664, 1096874, 3960906, 14299036, 51633110, 186437376, 673147554, 2430568646, 8776143806, 31687921122, 114416191032, 413124704992, 1491673030176, 5386005309890, 19447328987316

Offset

1,1

Comments

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

Column 2 of A196856.

Links

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

Formula

Empirical: a(n) = a(n-1) + 4*a(n-2) + 17*a(n-3) + 10*a(n-4) - 3*a(n-5) + 2*a(n-6) + 2*a(n-7) for n>8.

Empirical g.f.: x*(2 + 9*x + 19*x^2 + 20*x^3 + x^4 + 2*x^5 + x^6 - 6*x^7) / (1 - x - 4*x^2 - 17*x^3 - 10*x^4 + 3*x^5 - 2*x^6 - 2*x^7). - Colin Barker, Mar 01 2018

Example

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

Crossrefs

Cf. A196856.

Sequence in context: A059673 A294152 A196701 * A203534 A166989 A143550

Adjacent sequences: A196847 A196848 A196849 * A196851 A196852 A196853

Keyword

nonn

Author

R. H. Hardin, Oct 06 2011

Status

approved