A268069 Number of n X 1 0..3 arrays with every repeated value in every row and column unequal to the previous repeated value, and new values introduced in row-major sequential order.

1, 2, 4, 12, 39, 138, 499, 1830, 6723, 24714, 90751, 332910, 1219947, 4466562, 16340935, 59746326, 218334531, 797537226, 2912254303, 10631252766, 38800597851, 141582417426, 516549545527, 1884336977574, 6873201390579

Offset

1,2

Comments

Column 1 of A268073.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 3*a(n-2) - 30*a(n-3) + 28*a(n-4) + 36*a(n-5) - 36*a(n-6) for n>8.

Empirical g.f.: x*(1 - 4*x - 5*x^2 + 24*x^3 + 11*x^4 - 32*x^5 + 12*x^7) / ((1 - x)*(1 - 3*x)*(1 - 2*x^2)*(1 - 2*x - 6*x^2)). - Colin Barker, Feb 26 2018

Example

Some solutions for n=7:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....1....1....1....0....1....1....1....1....1....1....1....0....1
..2....1....1....2....2....1....1....2....1....0....0....2....2....1....1....2
..3....0....1....1....0....0....1....3....2....2....1....0....3....2....2....1
..3....0....0....3....1....0....0....3....1....1....0....0....3....1....3....2
..1....2....2....3....2....2....0....0....3....1....2....1....0....3....3....0
..3....3....3....1....2....0....2....2....1....3....1....3....3....0....1....0

Crossrefs

Cf. A268073.

Sequence in context: A341240 A108532 A213058 * A215071 A180487 A000940

Adjacent sequences: A268066 A268067 A268068 * A268070 A268071 A268072

Keyword

nonn

Author

R. H. Hardin, Jan 25 2016

Status

approved