A199705 Number of -n..n arrays x(0..2) of 3 elements with zero sum and no two neighbors equal.

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

R. H. Hardin, Table of n, a(n) for n = 1..200

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

Adjacent sequences: A199702 A199703 A199704 * A199706 A199707 A199708

Keyword

nonn

Author

R. H. Hardin, Nov 09 2011

Status

approved