A229666 Number of defective 4-colorings of an n X 2 0..3 array connected horizontally, antidiagonally and vertically with exactly two mistakes, and colors introduced in row-major 0..3 order.

0, 4, 61, 652, 5048, 33152, 197248, 1098752, 5838848, 29949952, 149454848, 729546752, 3497525248, 16517169152, 77015810048, 355207217152, 1622826549248, 7352984010752, 33073395662848, 147798414589952, 656648959950848

Offset

1,2

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3) for n>6.

Conjectures from Colin Barker, Sep 20 2018: (Start)

G.f.: x^2*(4 + 13*x + 112*x^2 - 104*x^3 - 32*x^4) / (1 - 4*x)^3.

a(n) = 2^(2*n-7) * (106 - 145*n + 50*n^2) for n>3.

(End)

Example

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

Crossrefs

Column 2 of A229672.

Sequence in context: A118005 A132064 A378553 * A252973 A262654 A218472

Adjacent sequences: A229663 A229664 A229665 * A229667 A229668 A229669

Keyword

nonn

Author

R. H. Hardin, Sep 27 2013

Status

approved