A196781 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,4,3,0,1 for x=0,1,2,3,4.

1, 3, 17, 39, 135, 427, 1351, 4319, 13715, 43607, 138727, 441175, 1403139, 4462583, 14192759, 45138911, 143560379, 456581095, 1452116295, 4618328471, 14688188867, 46714497719, 148571365447, 472518206415, 1502802742427, 4779532410183

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

Column 3 of A196786.

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) +4*a(n-3) +3*a(n-4) +6*a(n-5) +2*a(n-6) -2*a(n-7).

Empirical g.f.: x*(1 + x + 9*x^2 - 5*x^3 + 8*x^4 - 4*x^5) / (1 - 2*x - 2*x^2 - 4*x^3 - 3*x^4 - 6*x^5 - 2*x^6 + 2*x^7). - Colin Barker, May 09 2018

Example

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

Crossrefs

Cf. A196786.

Sequence in context: A073162 A146186 A179783 * A298232 A340463 A107147

Adjacent sequences: A196778 A196779 A196780 * A196782 A196783 A196784

Keyword

nonn

Author

R. H. Hardin, Oct 06 2011

Status

approved