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%I #8 May 20 2018 15:05:53
%S 0,80,520,1830,4750,10250,19530,34020,55380,85500,126500,180730,
%T 250770,339430,449750,585000,748680,944520,1176480,1448750,1765750,
%U 2132130,2552770,3032780,3577500,4192500,4883580,5656770,6518330,7474750,8532750
%N Number of -n..n arrays x(0..4) of 5 elements with zero sum and no two or three adjacent elements summing to zero.
%C Row 2 of A200430.
%H R. H. Hardin, <a href="/A200432/b200432.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = (115/12)*n^4 - (65/6)*n^3 + (65/12)*n^2 - (25/6)*n.
%F Conjectures from _Colin Barker_, May 20 2018: (Start)
%F G.f.: 10*x^2*(8 + 12*x + 3*x^2) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F (End)
%e Some solutions for n=3:
%e .-3...-2...-2...-2....1....0....1....3....1....0...-3...-3....0....2....1...-3
%e .-2....0....3....1....1...-2....0....0...-2...-1....1...-2....2....0....2...-1
%e ..3....3....0....0....1...-2....2....1...-2...-2....1....3...-1....1....1....0
%e ..3...-1...-2....1...-3....1...-1...-3....3....0....2....2....0....0...-2....2
%e .-1....0....1....0....0....3...-2...-1....0....3...-1....0...-1...-3...-2....2
%Y Cf. A200430.
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 17 2011
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