A239530 Number of (n+1) X (1+1) 0..2 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..2 introduced in row major order.

1, 1, 6, 13, 47, 128, 405, 1181, 3598, 10705, 32259, 96544, 290009, 869417, 2609238, 7826117, 23480935, 70438624, 211322637, 633956965, 1901888606, 5705637161, 17116957851, 51350798528, 154052516977, 462157354513, 1386472381350

Offset

1,3

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 3*a(n-3).

Conjectures from Colin Barker, Oct 26 2018: (Start)

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

a(n) = (10*3^n + 2^(-n)*((-1+sqrt(5))^n*(-5+4*sqrt(5)) - (-1-sqrt(5))^n*(5+4*sqrt(5)))) / 55.

(End)

Example

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

Crossrefs

Column 1 of A239537.

Sequence in context: A100905 A353964 A041489 * A131188 A247939 A203977

Adjacent sequences: A239527 A239528 A239529 * A239531 A239532 A239533

Keyword

nonn

Author

R. H. Hardin, Mar 21 2014

Status

approved