A184045 1/9 the number of (n+1) X 7 0..2 arrays with all 2 X 2 subblocks having the same four values.

153, 159, 169, 189, 225, 297, 433, 705, 1233, 2289, 4369, 8529, 16785, 33297, 66193, 131985, 263313, 525969, 1050769, 2100369, 4198545, 8394897, 16785553, 33566865, 67125393, 134242449, 268468369, 536920209, 1073807505, 2147582097, 4295098513

Offset

1,1

Comments

Column 6 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*(153 - 300*x - 308*x^2 + 600*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 3*2^(n/2) + 2^(n+1) + 145 for n even.

a(n) = 2^(n+1) + 2^((n+3)/2) + 145 for n odd.

(End)

Example

Some solutions for 5 X 7:
..2..1..0..1..2..1..2....2..1..2..1..2..1..2....1..2..2..0..2..0..2
..0..2..2..2..0..2..0....2..1..2..1..2..1..2....2..0..1..2..1..2..1
..2..1..0..1..2..1..2....1..2..1..2..1..2..1....1..2..2..0..2..0..2
..0..2..2..2..0..2..0....2..1..2..1..2..1..2....2..0..1..2..1..2..1
..2..1..0..1..2..1..2....2..1..2..1..2..1..2....1..2..2..0..2..0..2

Crossrefs

Cf. A184048.

Sequence in context: A346630 A165340 A183985 * A203603 A272767 A104810

Adjacent sequences: A184042 A184043 A184044 * A184046 A184047 A184048

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved