A197666 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

3, 9, 22, 71, 217, 642, 1963, 5963, 18018, 54753, 166329, 504940, 1534985, 4667983, 14198968, 43215503, 131584139, 400800484, 1221337807, 3723140135, 11353757744, 34635822651, 105696236527, 322652635812, 985253141189, 3009481166143

Offset

1,1

Comments

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

Column 2 of A197672.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +4*a(n-2) -25*a(n-4) -37*a(n-5) +4*a(n-6) +23*a(n-7) +17*a(n-8) -5*a(n-9) -a(n-10).

Empirical g.f.: x*(1 - x)*(1 + x)^2*(3 - 3*x - 11*x^2 - 20*x^3 - 3*x^4 + 15*x^5 + 2*x^6) / ((1 - x - 5*x^2 - 4*x^3 - x^4 + x^5)*(1 - 2*x - x^2 - 7*x^3 + 6*x^4 + x^5)). - Colin Barker, May 14 2018

Example

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

Crossrefs

Cf. A197672.

Sequence in context: A329163 A296582 A203454 * A146009 A326007 A272559

Adjacent sequences: A197663 A197664 A197665 * A197667 A197668 A197669

Keyword

nonn

Author

R. H. Hardin, Oct 17 2011

Status

approved