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%I #5 Mar 31 2012 12:36:39
%S 0,23674,1432402,24220966,210222830,1206988576,5230842688,18491305412,
%T 56022717236,150412523630,366439267062,824236891962,1734285496242,
%U 3448292160196,6530868950100,11857838629608,20748002017096
%N Number of -n..n arrays x(0..9) of 10 elements with zero sum and no two or three adjacent elements summing to zero
%C Row 7 of A200430
%H R. H. Hardin, <a href="/A200437/b200437.txt">Table of n, a(n) for n = 1..34</a>
%F Empirical: a(n) = (124952/567)*n^9 - (282778/315)*n^8 + (4520071/1890)*n^7 - (849277/180)*n^6 + (731309/108)*n^5 - (629357/90)*n^4 + (55560059/11340)*n^3 - (870757/420)*n^2 + (50299/126)*n
%e Some solutions for n=3
%e .-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3
%e .-2...-2...-3...-3...-2...-2...-3...-2...-1...-3...-1...-1...-3...-2...-3...-2
%e .-2....0....1....0....1...-3....2....0....0....1....2....0....1...-2....0...-2
%e .-2...-2...-2....2....0....1....0....3...-1....1....1...-3....0....0....1....0
%e ..1...-3...-1....2....3...-2....1....0...-1....1....3....0....1....3...-3...-1
%e ..2....1....0....2....0....3....1...-2....0....1...-2...-1....3....1...-2...-3
%e ..1....3....2...-3...-2....3....3....1....3...-3....3....2...-2....2....3....2
%e ..3....3....3....2....1...-1...-2....2....1....1....1....1....0....2....3....3
%e ..0....1....3....2....0....3....0...-1....2....3...-2....2....1....2....3....3
%e ..2....2....0...-1....2....1....1....2....0....1...-2....3....2...-3....1....3
%K nonn
%O 1,2
%A _R. H. Hardin_ Nov 17 2011