A184043 1/9 the number of (n+1) X 5 0..2 arrays with all 2 X 2 subblocks having the same four values.

45, 51, 61, 81, 117, 189, 325, 597, 1125, 2181, 4261, 8421, 16677, 33189, 66085, 131877, 263205, 525861, 1050661, 2100261, 4198437, 8394789, 16785445, 33566757, 67125285, 134242341, 268468261, 536920101, 1073807397, 2147581989, 4295098405

Offset

1,1

Comments

Column 4 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*(45 - 84*x - 92*x^2 + 168*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 3*2^(n/2) + 2^(n+1) + 37 for n even.

a(n) = 2^(n+1) + 2^((n+3)/2) + 37 for n odd.

(End)

Example

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

Crossrefs

Cf. A184048.

Sequence in context: A274368 A214572 A295493 * A345482 A295802 A242267

Adjacent sequences: A184040 A184041 A184042 * A184044 A184045 A184046

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved