A199944 Number of -n..n arrays x(0..2) of 3 elements with zeroth through 2nd differences all nonzero.

2, 36, 142, 376, 778, 1404, 2294, 3504, 5074, 7060, 9502, 12456, 15962, 20076, 24838, 30304, 36514, 43524, 51374, 60120, 69802, 80476, 92182, 104976, 118898, 134004, 150334, 167944, 186874, 207180, 228902, 252096, 276802, 303076, 330958, 360504

Offset

1,1

Comments

Row 3 of A199943.

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 + 15*x + 19*x^2 + 13*x^3) / ((1 - x)^4*(1 + x)).

a(n) = 6*n - 10*n^2 + 8*n^3 for n even.

a(n) = -2 + 6*n - 10*n^2 + 8*n^3 for n odd.

(End)

Example

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

Crossrefs

Cf. A199943.

Sequence in context: A187509 A134785 A143745 * A357445 A227927 A007757

Adjacent sequences: A199941 A199942 A199943 * A199945 A199946 A199947

Keyword

nonn

Author

R. H. Hardin, Nov 12 2011

Status

approved