A197058 Number of n X 5 0..4 arrays with each element equal to the number its horizontal and vertical neighbors equal to 2.

1, 5, 14, 28, 48, 90, 200, 447, 937, 1881, 3813, 7947, 16720, 34862, 71998, 148612, 308152, 640701, 1330955, 2759769, 5719391, 11860647, 24611330, 51069476, 105937956, 219719928, 455740768, 945408061, 1961252075, 4068435185

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 5 of A197061.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) +2*a(n-4) +3*a(n-5) -a(n-6) -2*a(n-7) -2*a(n-8) +2*a(n-9) -2*a(n-10) -a(n-11) -3*a(n-12) -a(n-13).

Empirical g.f.: x*(1 + 3*x + 5*x^2 + 4*x^3 - x^4 - 5*x^5 - 2*x^6 - 2*x^7 - x^8 - 6*x^9 - 5*x^10 - 4*x^11 - x^12) / (1 - 2*x + x^2 - x^3 - 2*x^4 - 3*x^5 + x^6 + 2*x^7 + 2*x^8 - 2*x^9 + 2*x^10 + x^11 + 3*x^12 + x^13). - Colin Barker, May 11 2018

Example

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

Crossrefs

Cf. A197061.

Sequence in context: A134238 A024800 A005586 * A212678 A244100 A031333

Adjacent sequences: A197055 A197056 A197057 * A197059 A197060 A197061

Keyword

nonn

Author

R. H. Hardin, Oct 09 2011

Status

approved