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A200058
Number of -n..n arrays x(0..3) of 4 elements with zero sum and elements alternately strictly increasing and strictly decreasing.
1
4, 26, 78, 172, 324, 546, 850, 1252, 1764, 2398, 3170, 4092, 5176, 6438, 7890, 9544, 11416, 13518, 15862, 18464, 21336, 24490, 27942, 31704, 35788, 40210, 44982, 50116, 55628, 61530, 67834, 74556, 81708, 89302, 97354, 105876, 114880, 124382, 134394
OFFSET
1,1
COMMENTS
Row 4 of A200057.
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) -3*a(n-2) +2*a(n-3) -3*a(n-4) +3*a(n-5) -a(n-6).
Empirical g.f.: 2*x*(2 + x + x^2)*(1 + 3*x + x^2) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, May 17 2018
EXAMPLE
Some solutions for n=6:
..2....6...-2....5....6...-2....2...-3....5....2....1....0....3....2....1....6
..5...-6...-3...-2...-4...-3...-4...-4...-5....0....3...-5...-3...-1...-4...-3
.-5....3....5....1....1....3....6....6....6....1...-3....5....1....0....5....0
.-2...-3....0...-4...-3....2...-4....1...-6...-3...-1....0...-1...-1...-2...-3
CROSSREFS
Cf. A200057.
Sequence in context: A099442 A014450 A283573 * A142962 A247194 A102198
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 13 2011
STATUS
approved