A229749 Number of defective 4-colorings of an n X 2 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..3 order.

0, 3, 60, 422, 1840, 6456, 20032, 57440, 155904, 406400, 1027072, 2532864, 6123520, 14563328, 34160640, 79192064, 181731328, 413368320, 932970496, 2091253760, 4658823168, 10321657856, 22754099200, 49935286272, 109135790080

Offset

1,2

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.

Conjectures from Colin Barker, Sep 21 2018: (Start)

G.f.: x^2*(3 + 42*x + 98*x^2 + 4*x^3) / (1 - 2*x)^3.

a(n) = 2^(n-3) * (195 - 192*n + 49*n^2) for n>2.

(End)

Example

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

Crossrefs

Column 2 of A229755.

Sequence in context: A081853 A183286 A195560 * A283381 A002738 A006432

Adjacent sequences: A229746 A229747 A229748 * A229750 A229751 A229752

Keyword

nonn

Author

R. H. Hardin, Sep 28 2013

Status

approved