A239024 Number of n X 2 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

1, 3, 4, 11, 16, 43, 64, 171, 256, 683, 1024, 2731, 4096, 10923, 16384, 43691, 65536, 174763, 262144, 699051, 1048576, 2796203, 4194304, 11184811, 16777216, 44739243, 67108864, 178956971, 268435456, 715827883, 1073741824, 2863311531, 4294967296

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 5*a(n-2) - 4*a(n-4).

Conjectures from Colin Barker, Oct 25 2018: (Start)

G.f.: x*(1 + 3*x - x^2 - 4*x^3) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)).

a(n) = (2 + (-2)^n + 2*(-1)^n + 7*2^n) / 12.

(End)

Example

Some solutions for n=5:
..2..0....2..0....2..0....2..0....2..0....2..0....2..0....2..0....2..0....2..0
..1..0....2..0....2..0....2..0....1..2....1..0....1..0....2..0....2..0....1..0
..2..0....1..2....1..0....1..2....2..1....2..0....2..0....1..2....1..2....2..0
..2..0....2..1....1..0....1..2....1..0....1..0....1..2....2..1....1..2....2..0
..1..2....1..2....2..0....2..1....2..0....2..0....2..1....1..0....2..0....1..0

Crossrefs

Column 2 of A239030.

Sequence in context: A007382 A127804 A027306 * A026676 A142870 A324552

Adjacent sequences: A239021 A239022 A239023 * A239025 A239026 A239027

Keyword

nonn

Author

R. H. Hardin, Mar 09 2014

Status

approved