A197174 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,2,1,0,0 for x=0,1,2,3,4.

1, 5, 10, 23, 58, 144, 363, 917, 2321, 5878, 14889, 37722, 95576, 242163, 613583, 1554685, 3939236, 9981179, 25290188, 64079982, 162365107, 411398825, 1042397613, 2641215094, 6692280455, 16956823380, 42965004446, 108864235075

Offset

1,2

Comments

Every 0 is next to 0 2'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 0's.

Column 2 of A197180.

Links

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

Formula

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

Empirical g.f.: x*(1 + x)*(1 + 2*x - 3*x^2 - x^3 - 6*x^4 + 3*x^6) / (1 - 2*x - x^2 - 2*x^3 + x^4 + 4*x^5 + 2*x^6 - x^7 - x^8). - Colin Barker, May 11 2018

Example

Some solutions for n=4:
..0..0....0..0....1..2....1..2....0..0....1..2....1..0....2..1....2..1....0..1
..0..3....0..0....0..1....0..1....0..0....0..1....2..1....1..0....1..0....1..2
..3..0....0..1....0..0....3..0....3..0....1..0....2..1....0..1....1..0....1..2
..0..0....1..2....0..0....0..0....0..0....2..1....1..0....1..2....2..1....0..1

Crossrefs

Cf. A197180.

Sequence in context: A295731 A175661 A355552 * A098112 A237435 A280721

Adjacent sequences: A197171 A197172 A197173 * A197175 A197176 A197177

Keyword

nonn

Author

R. H. Hardin, Oct 11 2011

Status

approved