A199910 Number of -n..n arrays x(0..2) of 3 elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

6, 12, 24, 42, 60, 84, 114, 144, 180, 222, 264, 312, 366, 420, 480, 546, 612, 684, 762, 840, 924, 1014, 1104, 1200, 1302, 1404, 1512, 1626, 1740, 1860, 1986, 2112, 2244, 2382, 2520, 2664, 2814, 2964, 3120, 3282, 3444, 3612, 3786, 3960, 4140, 4326, 4512

Offset: 1

Author

R. H. Hardin, Nov 11 2011

Keywords

• nonn

Comments

Row 3 of A199909.

Examples

			Some solutions for n=6:
..0...-1....4....6...-1....4...-3...-6....6...-2....2....3...-5....6....2...-2
.-5....1...-6...-2....0...-1....1....1...-4....5...-2...-2....3...-5...-5....2
..5....0....2...-4....1...-3....2....5...-2...-3....0...-1....2...-1....3....0
		

Links

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

Crossrefs

Cf. A199909.

Formula

Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5).

Empirical g.f.: 6*x*(1 + x^2) / ((1 - x)^3*(1 + x + x^2)). - Colin Barker, May 17 2018