A184032 1/16 the number of (n+1) X 3 0..3 arrays with all 2 X 2 subblocks having the same four values.

28, 40, 61, 103, 181, 337, 637, 1237, 2413, 4765, 9421, 18733, 37261, 74317, 148237, 296077, 591373, 1181965, 2362381, 4723213, 9443341, 18883597, 37761037, 75515917, 151019533, 302026765, 604028941, 1208033293, 2416017421, 4831985677

Offset

1,1

Comments

Column 2 of A184039.

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*(28 - 44*x - 59*x^2 + 88*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 13 for n even.

a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 13 for n odd.

(End)

Example

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

Crossrefs

Cf. A184039.

Sequence in context: A216594 A324858 A084807 * A361855 A047630 A135789

Adjacent sequences: A184029 A184030 A184031 * A184033 A184034 A184035

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved