login
A199705
Number of -n..n arrays x(0..2) of 3 elements with zero sum and no two neighbors equal.
1
6, 14, 32, 52, 82, 114, 156, 200, 254, 310, 376, 444, 522, 602, 692, 784, 886, 990, 1104, 1220, 1346, 1474, 1612, 1752, 1902, 2054, 2216, 2380, 2554, 2730, 2916, 3104, 3302, 3502, 3712, 3924, 4146, 4370, 4604, 4840, 5086, 5334, 5592, 5852, 6122, 6394, 6676
OFFSET
1,1
COMMENTS
Row 3 of A199704.
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
Conjectures from Colin Barker, May 16 2018: (Start)
G.f.: 2*x*(3 + x + 2*x^2) / ((1 - x)^3*(1 + x)).
a(n) = n + 3*n^2 for n even.
a(n) = 2 + n + 3*n^2 for n odd.
(End)
EXAMPLE
Some solutions for n=5:
..1...-5....1....1....3...-1...-2....3....1....2....2...-5....3...-3...-3....4
..3....3...-5....4....0...-4....3...-3...-1...-5....0....5...-2....4....0....1
.-4....2....4...-5...-3....5...-1....0....0....3...-2....0...-1...-1....3...-5
CROSSREFS
Cf. A199704.
Sequence in context: A024932 A273365 A271996 * A225972 A332724 A078836
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 09 2011
STATUS
approved