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

1,1

Comments

Row 3 of A200165.

Links

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

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)

Example

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

Crossrefs

Cf. A200165.

Sequence in context: A337397 A263226 A200821 * A226407 A226336 A213826

Adjacent sequences: A200163 A200164 A200165 * A200167 A200168 A200169

Keyword

nonn

Author

R. H. Hardin, Nov 13 2011

Status

approved