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A199944
Number of -n..n arrays x(0..2) of 3 elements with zeroth through 2nd differences all nonzero.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 12 2011
STATUS
approved