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

1,1

Comments

Row 4 of A200192.

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

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

Example

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

Crossrefs

Cf. A200192.

Sequence in context: A324915 A281760 A197885 * A188571 A083102 A270666

Adjacent sequences: A200190 A200191 A200192 * A200194 A200195 A200196

Keyword

nonn

Author

R. H. Hardin, Nov 14 2011

Status

approved