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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

%I #9 May 20 2018 11:32:31

%S 2,14,48,120,242,426,688,1040,1494,2066,2768,3612,4614,5786,7140,8692,

%T 10454,12438,14660,17132,19866,22878,26180,29784,33706,37958,42552,

%U 47504,52826,58530,64632,71144,78078,85450,93272,101556,110318,119570,129324

%N 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.

%C Row 4 of A200192.

%C 4th difference is 0 4 -4 0 4 -4 0 4 -4 0 4 -4.

%H R. H. Hardin, <a href="/A200193/b200193.txt">Table of n, a(n) for n = 1..200</a>

%F 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).

%F 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

%e Some solutions for n=5:

%e .-3....2...-2....0....0...-2....1....1...-2....5...-3...-3....0...-2...-1...-1

%e ..2...-5....5...-4....5....0...-5...-3....5...-5....5...-5...-2....3...-4....2

%e .-4....3...-3....5...-4...-3....3....3...-5....1...-4....5....4...-4....4...-3

%e ..5....0....0...-1...-1....5....1...-1....2...-1....2....3...-2....3....1....2

%Y Cf. A200192.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 14 2011