A200166 Number of -n..n arrays x(0..2) of 3 elements with nonzero sum and with zero through 2 differences all nonzero.

2, 34, 128, 348, 726, 1326, 2180, 3352, 4874, 6810, 9192, 12084, 15518, 19558, 24236, 29616, 35730, 42642, 50384, 59020, 68582, 79134, 90708, 103368, 117146, 132106, 148280, 165732, 184494, 204630, 226172, 249184, 273698, 299778, 327456, 356796

Offset: 1

Author

R. H. Hardin, Nov 13 2011

Keywords

• nonn

Comments

Row 3 of A200165.

Examples

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

Links

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

Crossrefs

Cf. A200165.

Formula

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

Conjectures from Colin Barker, May 17 2018: (Start)

G.f.: 2*x*(1 + 14*x + 15*x^2 + 18*x^3) / ((1 - x)^4*(1 + x)).

a(n) = 11*n - 13*n^2 + 8*n^3 for n even.

a(n) = -4 + 11*n - 13*n^2 + 8*n^3 for n odd.

(End)