A204699 Number of n X 2 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

2, 14, 96, 726, 5400, 40344, 301056, 2247264, 16773504, 125199744, 934502400, 6975223296, 52063770624, 388609284096, 2900619165696, 21650516238336, 161601653145600, 1206211160408064, 9003282670288896, 67201416721465344

Offset

1,1

Comments

Column 2 of A204705.

Links

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

Formula

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

Empirical g.f.: 2*x*(1 - 2*x)*(1 + 3*x - x^3) / ((1 + 2*x)*(1 - 8*x + 4*x^2)). - Colin Barker, Feb 23 2018

Example

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

Crossrefs

Cf. A204705.

Sequence in context: A164891 A141146 A267913 * A286445 A322262 A109808

Adjacent sequences: A204696 A204697 A204698 * A204700 A204701 A204702

Keyword

nonn

Author

R. H. Hardin, Jan 18 2012

Status

approved