A197368 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,4,1,0,1 for x=0,1,2,3,4.

1, 3, 32, 45, 189, 646, 1873, 6209, 19883, 62891, 201940, 644884, 2058462, 6580709, 21022103, 67159181, 214583759, 685563259, 2190314160, 6997940987, 22357818950, 71431546562, 228218559544, 729140737836, 2329549699706, 7442735684274

Offset

1,2

Comments

Every 0 is next to 0 2's, every 1 is next to 1 4'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 3 of A197373.

Links

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

Formula

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

Empirical g.f.: x*(1 + x + 24*x^2 - 32*x^3 + 17*x^4 - 37*x^5 - 9*x^6 + 9*x^7) / (1 - 2*x - 2*x^2 - 7*x^3 + 3*x^4 + 7*x^6 + 5*x^7 - 3*x^8). - Colin Barker, May 12 2018

Example

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

Crossrefs

Cf. A197373.

Sequence in context: A254312 A304048 A324223 * A114257 A197524 A107465

Adjacent sequences: A197365 A197366 A197367 * A197369 A197370 A197371

Keyword

nonn

Author

R. H. Hardin, Oct 14 2011

Status

approved