A196804 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,3,0,1 for x=0,1,2,3,4.

1, 3, 16, 37, 120, 420, 1468, 4801, 15885, 53128, 178165, 594582, 1983454, 6622194, 22119691, 73864009, 246623786, 823483995, 2749775102, 9181948002, 30659615818, 102376096183, 341847401583, 1141474348346, 3811532000911, 12727199593820

Offset

1,2

Comments

Every 0 is next to 0 4'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 1's.

Column 3 of A196809.

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) +17*a(n-4) +3*a(n-5) -4*a(n-6).

Empirical g.f.: x*(1 + x + 8*x^2 - 4*x^3 - 12*x^4 + 4*x^5) / (1 - 2*x - 2*x^2 - 3*x^3 - 17*x^4 - 3*x^5 + 4*x^6). - Colin Barker, May 09 2018

Example

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

Crossrefs

Cf. A196809.

Sequence in context: A294419 A196596 A196573 * A280093 A081270 A271374

Adjacent sequences: A196801 A196802 A196803 * A196805 A196806 A196807

Keyword

nonn

Author

R. H. Hardin, Oct 06 2011

Status

approved