A268419 Number of n X 1 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

1, 2, 5, 14, 44, 147, 505, 1750, 6065, 20950, 72052, 246715, 841345, 2858714, 9682221, 32700942, 110173948, 370393059, 1242869721, 4163561358, 13927246329, 46526402422, 155249799428, 517505902283, 1723457914689, 5734951039346

Offset

1,2

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 20*a(n-2) + 12*a(n-3) + 12*a(n-4) - 8*a(n-5) - 3*a(n-6).

Empirical g.f.: x*(1 - 6*x + 9*x^2 + 2*x^3 - 4*x^4 - x^5) / ((1 - x)*(1 - 3*x)*(1 - x - x^2)*(1 - 3*x - x^2)). - Colin Barker, Jan 13 2019

Example

Some solutions for n=8:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....1....0....1....1....1....1....0....1....1....1....1....0....1
..0....2....1....2....0....0....1....2....0....1....0....2....0....2....0....0
..1....2....0....2....0....1....1....1....2....2....2....0....2....1....1....1
..2....3....2....1....0....2....0....2....3....0....1....0....0....3....0....1
..0....0....3....0....0....1....1....3....3....2....3....2....3....0....2....1
..3....2....0....3....0....0....2....3....3....0....1....0....2....2....1....2
..0....2....3....2....1....3....3....2....1....1....0....2....2....0....0....1

Crossrefs

Column 1 of A268423.

Sequence in context: A306799 A369590 A148335 * A149883 A307786 A360592

Adjacent sequences: A268416 A268417 A268418 * A268420 A268421 A268422

Keyword

nonn

Author

R. H. Hardin, Feb 04 2016

Status

approved