A204678 Number of n X 1 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

1, 2, 4, 12, 40, 143, 528, 1979, 7466, 28246, 106992, 405481, 1537042, 5826959, 22091016, 83752328, 317527448, 1203835147, 4564081020, 17303737555, 65603438014, 248721498050, 942974761824, 3575088704597, 13554190277870

Offset

1,2

Comments

Column 1 of A204685.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + a(n-2) - 6*a(n-3) - 3*a(n-4) for n>6.

Empirical g.f.: x*(1 + x)*(1 - 3*x - 2*x^2 + 2*x^3 + x^4) / ((1 - x - x^2)*(1 - 3*x - 3*x^2)). - Colin Barker, Feb 19 2018

Example

Some solutions for n=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....0....1....0....0....1....0....1....0....0....0....1....1....0
..1....2....0....1....0....1....1....0....1....1....1....1....1....0....0....1
..0....1....2....0....0....0....0....1....0....0....0....1....0....0....0....0
..0....0....0....0....1....2....0....0....0....0....0....0....1....1....1....0

Crossrefs

Sequence in context: A056236 A300652 A028329 * A025227 A211965 A119430

Adjacent sequences: A204675 A204676 A204677 * A204679 A204680 A204681

Keyword

nonn

Author

R. H. Hardin, Jan 18 2012

Status

approved