A196324 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,0,4,2 for x=0,1,2,3,4.

2, 10, 27, 68, 206, 573, 1596, 4526, 12751, 35868, 101108, 284859, 802366, 2260510, 6368345, 17940394, 50541298, 142383741, 401118412, 1130018646, 3183454841, 8968329772, 25265303118, 71176638773, 200516638286, 564889314536

Offset

1,1

Comments

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

Column 3 of A196329.

Links

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

Formula

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

Empirical g.f.: x*(2 + 8*x + 11*x^2 + x^3 + x^4 - 8*x^6 - 6*x^7 - x^8) / ((1 + x)*(1 - 2*x - x^2 - 4*x^3 + x^4 - x^6 + x^7 + x^8)). - Colin Barker, May 08 2018

Example

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

Crossrefs

Cf. A196329.

Sequence in context: A099583 A328743 A133479 * A327841 A196648 A220700

Adjacent sequences: A196321 A196322 A196323 * A196325 A196326 A196327

Keyword

nonn

Author

R. H. Hardin, Oct 01 2011

Status

approved