A184041 1/9 the number of (n+1) X 3 0..2 arrays with all 2 X 2 subblocks having the same four values.

15, 21, 31, 51, 87, 159, 295, 567, 1095, 2151, 4231, 8391, 16647, 33159, 66055, 131847, 263175, 525831, 1050631, 2100231, 4198407, 8394759, 16785415, 33566727, 67125255, 134242311, 268468231, 536920071, 1073807367, 2147581959, 4295098375

Offset

1,1

Comments

Column 2 of A184048.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).

Conjectures from Colin Barker, Apr 10 2018: (Start)

G.f.: x*(15 - 24*x - 32*x^2 + 48*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 3*2^(n/2) + 2^(n+1) + 7 for n even.

a(n) = 2^(n+1) + 2^((n+3)/2) + 7 for n odd.

(End)

Example

Some solutions for 5 X 3:
..1..0..0....2..1..2....2..1..2....0..1..0....0..0..0....0..1..0....1..1..1
..0..1..1....0..0..0....1..1..1....0..2..0....1..1..1....1..2..1....0..1..0
..1..0..0....2..1..2....2..1..2....1..0..1....0..0..0....1..0..1....1..1..1
..0..1..1....0..0..0....1..1..1....0..2..0....1..1..1....2..1..2....0..1..0
..1..0..0....1..2..1....1..2..1....1..0..1....0..0..0....0..1..0....1..1..1

Crossrefs

Cf. A184048.

Sequence in context: A324110 A285800 A340380 * A070005 A275384 A185307

Adjacent sequences: A184038 A184039 A184040 * A184042 A184043 A184044

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved