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

1,1

Comments

Row 4 of A199530.

Links

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

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)

Example

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

Crossrefs

Cf. A199530.

Sequence in context: A340302 A143698 A304164 * A188660 A047928 A300847

Adjacent sequences: A199528 A199529 A199530 * A199532 A199533 A199534

Keyword

nonn

Author

R. H. Hardin, Nov 07 2011

Status

approved