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%I #9 May 21 2018 08:48:21
%S 0,212,2232,11008,36952,98052,221984,448224,830160,1437204,2356904,
%T 3697056,5587816,8183812,11666256,16245056,22160928,29687508,39133464,
%U 50844608,65206008,82644100,103628800,128675616,158347760,193258260
%N Number of -n..n arrays x(0..5) of 6 elements with zero sum and no two or three adjacent elements summing to zero.
%C Row 3 of A200430.
%H R. H. Hardin, <a href="/A200433/b200433.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = (88/5)*n^5 - (109/3)*n^4 + 44*n^3 - (107/3)*n^2 + (52/5)*n.
%F Conjectures from _Colin Barker_, May 21 2018: (Start)
%F G.f.: 4*x^2*(53 + 240*x + 199*x^2 + 36*x^3) / (1 - x)^6.
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F (End)
%e Some solutions for n=3:
%e ..0...-2....0....0....2...-1....0...-2....3....2....3....3....2...-1....3....1
%e ..2....0....2....3....0...-1...-2....3...-1....2....3...-1....3....3...-1....2
%e .-3....1....2...-1...-3....0....3....3...-1....2...-2....3....1....3...-3...-1
%e ..2....2...-3...-3....0...-1....1...-1...-2....0...-2....0...-2....0....0....0
%e .-1....0...-2...-2....2....3...-3...-1...-2...-3...-2...-2...-3...-2....2...-1
%e ..0...-1....1....3...-1....0....1...-2....3...-3....0...-3...-1...-3...-1...-1
%Y Cf. A200430.
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 17 2011
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