A196573 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,2,3,0,4 for x=0,1,2,3,4.

1, 3, 16, 37, 117, 372, 1168, 3613, 11247, 35047, 109150, 339828, 1058164, 3295056, 10260427, 31949551, 99486794, 309789423, 964645058, 3003782043, 9353396014, 29125288852, 90692454357, 282404795252, 879372700786, 2738255017364

Offset

1,2

Comments

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

Column 3 of A196578.

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) +3*a(n-3) +5*a(n-4) -a(n-6).

Empirical g.f.: x*(1 + x + 8*x^2 - 4*x^3 - 3*x^4 + x^5) / ((1 + x)*(1 - 3*x + x^2 - 4*x^3 - x^4 + x^5)). - Colin Barker, May 09 2018

Example

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

Crossrefs

Cf. A196578.

Sequence in context: A066875 A294419 A196596 * A196804 A280093 A081270

Adjacent sequences: A196570 A196571 A196572 * A196574 A196575 A196576

Keyword

nonn

Author

R. H. Hardin, Oct 04 2011

Status

approved