A184042 1/9 the number of (n+1) X 4 0..2 arrays with all 2 X 2 subblocks having the same four values.

25, 31, 41, 61, 97, 169, 305, 577, 1105, 2161, 4241, 8401, 16657, 33169, 66065, 131857, 263185, 525841, 1050641, 2100241, 4198417, 8394769, 16785425, 33566737, 67125265, 134242321, 268468241, 536920081, 1073807377, 2147581969, 4295098385

Offset

1,1

Comments

Column 3 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*(25 - 44*x - 52*x^2 + 88*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 3*2^(n/2) + 2^(n+1) + 17 for n even.

a(n) = 2^(n+1) + 2^((n+3)/2) + 17 for n odd.

(End)

Example

Some solutions for 5 X 4:
..2..1..2..1....0..2..0..2....2..2..2..0....1..1..1..1....0..2..0..2
..0..2..0..2....1..1..1..1....0..0..0..2....2..1..2..1....2..0..2..0
..1..2..1..2....2..0..2..0....2..2..2..0....1..1..1..1....0..2..0..2
..0..2..0..2....1..1..1..1....0..0..0..2....2..1..2..1....2..0..2..0
..1..2..1..2....2..0..2..0....2..2..2..0....1..1..1..1....2..0..2..0

Crossrefs

Cf. A184048.

Sequence in context: A213929 A167324 A307283 * A157646 A198003 A039323

Adjacent sequences: A184039 A184040 A184041 * A184043 A184044 A184045

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved