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A229572
Number of defective 4-colorings of an n X 2 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..3 order.
1
1, 6, 26, 80, 216, 544, 1312, 3072, 7040, 15872, 35328, 77824, 169984, 368640, 794624, 1703936, 3637248, 7733248, 16384000, 34603008, 72876032, 153092096, 320864256, 671088640, 1400897536, 2919235584, 6073352192, 12616466432, 26172456960
OFFSET
1,2
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) - 4*a(n-2) for n>3.
Conjectures from Colin Barker, Sep 19 2018: (Start)
G.f.: x*(1 + 2*x + 6*x^2) / (1 - 2*x)^2.
a(n) = 2^(n-2) * (7*n-8) for n>1. (End)
Conjectured e.g.f.: 2 + (3*x + exp(2*x)*(7*x - 4))/2. - Stefano Spezia, Oct 21 2022
EXAMPLE
Some solutions for n=3:
..0..1....0..1....0..0....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..2..2....2..0....1..2....2..2....2..1....2..2....2..2....2..3....2..1....2..2
..0..3....1..3....3..0....0..1....3..0....3..1....3..0....2..0....0..3....1..3
CROSSREFS
Column 2 of A229578.
Sequence in context: A286188 A335648 A094162 * A316160 A224035 A172207
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 26 2013
STATUS
approved