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

Author

R. H. Hardin, Nov 09 2011

Keywords

• nonn

Comments

Row 3 of A199704.

Examples

			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
		

Links

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

Crossrefs

Cf. A199704.

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)