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, 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

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

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

Adjacent sequences: A229569 A229570 A229571 * A229573 A229574 A229575

Keyword

nonn

Author

R. H. Hardin, Sep 26 2013

Status

approved