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A200058 Number of -n..n arrays x(0..3) of 4 elements with zero sum and elements alternately strictly increasing and strictly decreasing. 1

%I

%S 4,26,78,172,324,546,850,1252,1764,2398,3170,4092,5176,6438,7890,9544,

%T 11416,13518,15862,18464,21336,24490,27942,31704,35788,40210,44982,

%U 50116,55628,61530,67834,74556,81708,89302,97354,105876,114880,124382,134394

%N Number of -n..n arrays x(0..3) of 4 elements with zero sum and elements alternately strictly increasing and strictly decreasing.

%C Row 4 of A200057.

%H R. H. Hardin, <a href="/A200058/b200058.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*(2 + x + x^2)*(1 + 3*x + x^2) / ((1 - x)^4*(1 + x + x^2)). - _Colin Barker_, May 17 2018

%e Some solutions for n=6:

%e ..2....6...-2....5....6...-2....2...-3....5....2....1....0....3....2....1....6

%e ..5...-6...-3...-2...-4...-3...-4...-4...-5....0....3...-5...-3...-1...-4...-3

%e .-5....3....5....1....1....3....6....6....6....1...-3....5....1....0....5....0

%e .-2...-3....0...-4...-3....2...-4....1...-6...-3...-1....0...-1...-1...-2...-3

%Y Cf. A200057.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 13 2011

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Last modified September 17 05:34 EDT 2021. Contains 347478 sequences. (Running on oeis4.)