A184046 1/9 the number of (n+1) X 8 0..2 arrays with all 2 X 2 subblocks having the same four values.

289, 295, 305, 325, 361, 433, 569, 841, 1369, 2425, 4505, 8665, 16921, 33433, 66329, 132121, 263449, 526105, 1050905, 2100505, 4198681, 8395033, 16785689, 33567001, 67125529, 134242585, 268468505, 536920345, 1073807641, 2147582233, 4295098649

Offset

1,1

Comments

Column 7 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*(289 - 572*x - 580*x^2 + 1144*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 3*2^(n/2) + 2^(n+1) + 281 for n even.

a(n) = 2^(n+1) + 2^((n+3)/2) + 281 for n odd.

(End)

Example

Some solutions for 5 X 8:
..1..1..1..0..0..0..1..1....0..2..0..2..2..2..0..2....1..0..1..0..1..0..1..0
..0..0..0..1..1..1..0..0....2..1..2..1..0..1..2..1....2..1..2..1..2..1..2..1
..1..1..1..0..0..0..1..1....0..2..0..2..2..2..0..2....1..0..1..0..1..0..1..0
..0..0..0..1..1..1..0..0....2..1..2..1..0..1..2..1....1..2..1..2..1..2..1..2
..1..1..1..0..0..0..1..1....0..2..0..2..2..2..0..2....0..1..0..1..0..1..0..1

Crossrefs

Cf. A184048.

Sequence in context: A107739 A221203 A188367 * A235810 A229906 A008367

Adjacent sequences: A184043 A184044 A184045 * A184047 A184048 A184049

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved