A199531 Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two consecutive zero elements.

12, 72, 212, 464, 860, 1432, 2212, 3232, 4524, 6120, 8052, 10352, 13052, 16184, 19780, 23872, 28492, 33672, 39444, 45840, 52892, 60632, 69092, 78304, 88300, 99112, 110772, 123312, 136764, 151160, 166532, 182912, 200332, 218824, 238420, 259152

Offset: 1

Author

R. H. Hardin, Nov 07 2011

Keywords

• nonn

Comments

Row 4 of A199530.

Examples

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

Links

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

Crossrefs

Cf. A199530.

Formula

Empirical: a(n) = (16/3)*n^3 + 8*n^2 - (4/3)*n.

Conjectures from Colin Barker, May 15 2018: (Start)

G.f.: 4*x*(3 + 6*x - x^2) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)