A229749 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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