A223057 Number of n X 3 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

5, 114, 4865, 213469, 9383963, 412602889, 18142309235, 797728639489, 35076656042963, 1542343995891289, 67817897342466755, 2981998328788355809, 131120462107713937763, 5765454466967090614489, 253510891259359153159475

Offset: 1

Author

R. H. Hardin, Mar 13 2013

Keywords

• nonn

Comments

Column 3 of A223062.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A223062.

Formula

Empirical: a(n) = 55*a(n-1) - 515*a(n-2) + 1337*a(n-3) - 696*a(n-4) - 1188*a(n-5) + 1008*a(n-6) for n>7.

Empirical g.f.: x*(5 - 161*x + 1170*x^2 - 2081*x^3 - 295*x^4 + 2238*x^5 - 336*x^6) / ((1 - x)*(1 - 2*x)*(1 - 52*x + 357*x^2 - 162*x^3 - 504*x^4)). - Colin Barker, Aug 17 2018