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A199839 Number of -n..n arrays x(0..9) of 10 elements with zero sum and no two neighbors summing to zero.

%I A199839 #10 Jul 22 2025 13:24:52
%S A199839 138,88636,3685550,51077518,389832124,2044221894,8281149188,
%T A199839 27785393300,80752300406,209581305608,496408914210,1090354976530,
%U A199839 2248071267000,4391976524034,8191437222152,14673108432136,25367684178562
%N A199839 Number of -n..n arrays x(0..9) of 10 elements with zero sum and no two neighbors summing to zero.
%C A199839 Row 8 of A199832
%H A199839 R. H. Hardin, <a href="/A199839/b199839.txt">Table of n, a(n) for n = 1..33</a>
%F A199839 Empirical: a(n) = (124952/567)*n^9 - (35524/315)*n^8 + (50588/945)*n^7 - (2494/45)*n^6 + (13739/270)*n^5 - (1927/180)*n^4 - (41254/2835)*n^3 + (3319/420)*n^2 - (781/630)*n
%e A199839 Some.solutions.for.n=3
%e A199839 .-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3...-3
%e A199839 .-3...-2...-3...-3...-2...-3...-2...-3...-3...-3...-3...-2...-3...-3...-3...-2
%e A199839 ..2....0....2...-1...-3....1....1....0....1....0....2....0....1....1....2....1
%e A199839 ..1...-1....3....2....1....1...-3....3...-2....2....0....1....1...-2....0....1
%e A199839 ..1....3....3....2....1....3....2....2....3....3....1...-2....2....3...-1....3
%e A199839 ..2...-1....2...-3....3....1....1....0....2....3....1....3....0....3....3....1
%e A199839 .-3....0....1....1....3....3....1....1....3....0....1...-2...-3....0....2...-2
%e A199839 ..1....1....1....3....1....0....2...-2....0....1...-2....3....1....2....1...-2
%e A199839 ..1....3...-3....0....1...-2....0....1...-2...-2....3....3....1...-1...-2....1
%e A199839 ..1....0...-3....2...-2...-1....1....1....1...-1....0...-1....3....0....1....2
%K A199839 nonn
%O A199839 1,1
%A A199839 _R. H. Hardin_ Nov 11 2011