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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, 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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 21 2014
STATUS
approved