|
|
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.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
4th difference is 0 4 -4 0 4 -4 0 4 -4 0 4 -4.
|
|
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*(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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|