A200058 Number of -n..n arrays x(0..3) of 4 elements with zero sum and elements alternately strictly increasing and strictly decreasing.

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

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

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

Adjacent sequences: A200055 A200056 A200057 * A200059 A200060 A200061

Keyword

nonn

Author

R. H. Hardin, Nov 13 2011

Status

approved