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%I #11 May 25 2021 05:11:21
%S 66,23206,645780,6715618,41008804,179213048,622300326,1827026482,
%T 4719970500,11025201168,23740333870,47800415256,90973748554,
%U 165038447302,287293180292,482460245532,785043786046,1242210635346,1917265955424
%N Number of -n..n arrays x(0..8) of 9 elements with zero sum and no two neighbors summing to zero.
%C Row 7 of A199832.
%H R. H. Hardin, <a href="/A199838/b199838.txt">Table of n, a(n) for n = 1..80</a>
%F Empirical: a(n) = (259723/2240)*n^8 - (299869/5040)*n^7 + (39757/1440)*n^6 - (8303/360)*n^5 + (31829/2880)*n^4 - (8083/720)*n^3 + (32213/5040)*n^2 - (509/420)*n.
%F Conjectures from _Colin Barker_, Mar 02 2018: (Start)
%F G.f.: 2*x*(33 + 11306*x + 219651*x^2 + 866735*x^3 + 937667*x^4 + 283090*x^5 + 18897*x^6 + 128*x^7) / (1 - x)^9.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F (End)
%e Some solutions for n=3:
%e .-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3....0
%e .-3...-3...-3....2....2....2....2....1...-1....0...-1...-3....2....0....1...-3
%e .-1...-1....0....1...-1....0....0...-3...-1....2....0...-1....3....1...-2...-2
%e ..2....0...-3...-3...-2....1....2....1....2...-1....2...-1....1....2....1....3
%e ..0....2....2...-3....3...-3....0....3....2....0....2....3...-2....1....3...-1
%e .-1....0....3...-2....0...-1...-3...-1...-3...-3....0....3...-3....3...-1...-2
%e ..3....3....0....3...-1....2...-1....3....0....0....1....0....1....0....2....3
%e ..3....0....2....2....0....1....2....1....2....3...-2....3....2...-1....2...-1
%e ..0....2....2....3....2....1....1...-2....2....2....1...-1...-1...-3...-3....3
%Y Cf. A199832.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 11 2011