A197057 Number of n X 4 0..4 arrays with each element equal to the number its horizontal and vertical neighbors equal to 2.

1, 4, 10, 18, 28, 47, 93, 189, 357, 640, 1156, 2162, 4102, 7697, 14243, 26307, 48917, 91394, 170572, 317326, 589634, 1096821, 2042877, 3805343, 7083795, 13181280, 24530278, 45664276, 85014554, 158256855, 294565501, 548276423, 1020572419

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 2's, every 3 is next to 3 2's, every 4 is next to 4 2's.

Column 4 of A197061.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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

Empirical g.f.: x*(1 + x)*(1 + x + x^2)*(1 + x + 2*x^2 - x^4 - 2*x^5) / (1 - x - x^3 - 2*x^4 - 3*x^5 - 2*x^6 + x^7 + 3*x^8 + 2*x^9). - Colin Barker, May 11 2018

Example

Some solutions for n=5:
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..1..1..1....0..0..0..0....1..1..1..0....1..1..1..1....1..1..0..0
..1..2..2..2....0..0..0..0....2..2..2..1....2..2..2..2....2..2..1..0
..1..2..4..2....0..0..0..0....2..4..2..1....2..3..3..2....2..2..1..0
..1..2..2..2....0..0..0..0....2..2..2..1....2..2..2..2....1..1..0..0

Crossrefs

Cf. A197061.

Sequence in context: A028552 A009877 A009880 * A025712 A283969 A022781

Adjacent sequences: A197054 A197055 A197056 * A197058 A197059 A197060

Keyword

nonn

Author

R. H. Hardin, Oct 09 2011

Status

approved