A204679 Number of n X 2 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.

2, 15, 159, 2191, 31168, 447343, 6427791, 92387812, 1327953799, 19087798375, 274365294336, 3943689122935, 56686048473223, 814797524429284, 11711788424726319, 168343648648695295, 2419748633865949120

Offset

1,1

Comments

Column 2 of A204685.

Links

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

Formula

Empirical: a(n) = 14*a(n-1) +14*a(n-2) -124*a(n-3) -6*a(n-4) +90*a(n-5) -27*a(n-6) for n>8.

Empirical g.f.: x*(2 - 13*x - 79*x^2 + 3*x^3 + 140*x^4 - 57*x^5 - 21*x^6 + 9*x^7) / ((1 + x)*(1 + 3*x)*(1 - 3*x + x^2)*(1 - 15*x + 9*x^2)). - Colin Barker, Feb 23 2018

Example

Some solutions for n=5:
..0..1....0..0....0..1....0..0....0..0....0..0....0..0....0..0....0..1....0..0
..1..0....1..0....1..0....0..1....0..0....0..0....0..0....0..0....0..1....0..0
..0..0....0..1....0..0....1..2....1..2....1..1....1..1....1..2....1..0....1..1
..0..1....1..0....2..1....0..1....1..3....2..3....0..1....2..1....1..0....1..2
..1..0....0..1....0..2....0..0....2..0....3..0....1..2....1..0....2..3....2..0

Crossrefs

Cf. A204685.

Sequence in context: A324463 A139085 A268070 * A363564 A364331 A259608

Adjacent sequences: A204676 A204677 A204678 * A204680 A204681 A204682

Keyword

nonn

Author

R. H. Hardin, Jan 18 2012

Status

approved