A196976 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,2,1,0,4 for x=0,1,2,3,4.

1, 5, 14, 37, 104, 290, 803, 2233, 6207, 17242, 47913, 133140, 369944, 1027963, 2856397, 7937011, 22054470, 61282473, 170284722, 473167812, 1314784901, 3653374545, 10151581325, 28208058702, 78381342385, 217797151870

Offset

1,2

Comments

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

Column 2 of A196982.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + a(n-2) + 4*a(n-3) - 2*a(n-4) - a(n-6).

Empirical g.f.: x*(1 + x)^2*(1 + x - x^3) / (1 - 2*x - x^2 - 4*x^3 + 2*x^4 + x^6). - Colin Barker, Mar 01 2018

Example

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

Crossrefs

Cf. A196982.

Sequence in context: A127980 A054486 A072130 * A045553 A270687 A272254

Adjacent sequences: A196973 A196974 A196975 * A196977 A196978 A196979

Keyword

nonn

Author

R. H. Hardin, Oct 08 2011

Status

approved