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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
Row 4 of A200192.
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
Cf. A200192.
Sequence in context: A324915 A281760 A197885 * A188571 A083102 A270666
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 14 2011
STATUS
approved

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Last modified July 14 12:22 EDT 2024. Contains 374318 sequences. (Running on oeis4.)