A200193 Number of -n..n arrays x(0..3) of 4 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

2, 14, 48, 120, 242, 426, 688, 1040, 1494, 2066, 2768, 3612, 4614, 5786, 7140, 8692, 10454, 12438, 14660, 17132, 19866, 22878, 26180, 29784, 33706, 37958, 42552, 47504, 52826, 58530, 64632, 71144, 78078, 85450, 93272, 101556, 110318, 119570, 129324

Offset: 1

Author

R. H. Hardin, Nov 14 2011

Keywords

• nonn

Comments

Row 4 of A200192.

4th difference is 0 4 -4 0 4 -4 0 4 -4 0 4 -4.

Examples

			Some solutions for n=5:
.-3....2...-2....0....0...-2....1....1...-2....5...-3...-3....0...-2...-1...-1
..2...-5....5...-4....5....0...-5...-3....5...-5....5...-5...-2....3...-4....2
.-4....3...-3....5...-4...-3....3....3...-5....1...-4....5....4...-4....4...-3
..5....0....0...-1...-1....5....1...-1....2...-1....2....3...-2....3....1....2
		

Links

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

Crossrefs

Cf. A200192.

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*(1 + 3*x + x^2)*(1 + x + 2*x^2) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, May 20 2018