A200039 Number of -n..n arrays x(0..2) of 3 elements with sum zero and with zeroth through 2nd differences all nonzero.

0, 2, 14, 28, 52, 78, 114, 152, 200, 250, 310, 372, 444, 518, 602, 688, 784, 882, 990, 1100, 1220, 1342, 1474, 1608, 1752, 1898, 2054, 2212, 2380, 2550, 2730, 2912, 3104, 3298, 3502, 3708, 3924, 4142, 4370, 4600, 4840, 5082, 5334, 5588, 5852, 6118, 6394

Offset

1,2

Comments

Row 3 of A200038.

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 17 2018: (Start)

G.f.: 2*x^2*(1 + 5*x) / ((1 - x)^3*(1 + x)).

a(n) = -5*n + 3*n^2 for n even.

a(n) = 2 - 5*n + 3*n^2 for n odd.

(End)

Example

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

Crossrefs

Cf. A200038.

Sequence in context: A031079 A364764 A355864 * A281206 A189331 A157023

Adjacent sequences: A200036 A200037 A200038 * A200040 A200041 A200042

Keyword

nonn

Author

R. H. Hardin, Nov 12 2011

Status

approved