A206570 Number of n X 1 0..3 arrays avoiding the pattern z-1 z-1 z in any row, column or nw-to-se diagonal.

4, 16, 61, 232, 882, 3353, 12747, 48460, 184229, 700378, 2662606, 10122349, 38481829, 146295209, 556166085, 2114359836, 8038098037, 30558194945, 116172168341, 441648229594, 1679000758004, 6383006556982, 24266083569200

Offset

1,1

Comments

Column 1 of A206577.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 3*a(n-3) + 2*a(n-5) - a(n-7).

Empirical g.f.: x*(4 - 3*x^2 + 2*x^4 - x^6) / (1 - 4*x + 3*x^3 - 2*x^5 + x^7). - Colin Barker, Feb 20 2018

Example

Some solutions for n=4:
..1....1....2....0....0....1....0....3....0....1....1....0....1....2....1....1
..0....3....0....2....1....3....2....0....0....0....1....3....3....0....0....3
..0....2....1....2....1....0....1....3....2....1....0....1....3....1....1....2
..0....1....2....1....3....1....3....1....0....3....3....2....1....0....1....2

Crossrefs

Cf. A206577.

Sequence in context: A268452 A133161 A103820 * A206790 A283858 A283409

Adjacent sequences: A206567 A206568 A206569 * A206571 A206572 A206573

Keyword

nonn

Author

R. H. Hardin, Feb 09 2012

Status

approved