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A199836 Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two neighbors summing to zero.

%I A199836 #8 May 16 2018 11:19:41
%S A199836 22,1650,20240,118280,462234,1402934,3579520,8046928,16426926,
%T A199836 31082698,55316976,93593720,151783346,237431502,360051392,531439648,
%U A199836 766015750,1081184994,1497725008,2040195816,2737373450,3622707110,4734799872
%N A199836 Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two neighbors summing to zero.
%C A199836 Row 5 of A199832.
%H A199836 R. H. Hardin, <a href="/A199836/b199836.txt">Table of n, a(n) for n = 1..200</a>
%F A199836 Empirical: a(n) = (5887/180)*n^6 - (1013/60)*n^5 + (245/36)*n^4 - (35/12)*n^3 + (157/45)*n^2 - (6/5)*n.
%F A199836 Conjectures from _Colin Barker_, May 16 2018: (Start)
%F A199836 G.f.: 2*x*(11 + 748*x + 4576*x^2 + 5240*x^3 + 1167*x^4 + 32*x^5) / (1 - x)^7.
%F A199836 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A199836 (End)
%e A199836 Some solutions for n=3:
%e A199836 ..0....1...-2...-1...-1....3....0....1...-1....1...-2...-2....0....2...-1....0
%e A199836 .-1....0....1...-1...-2....1....3....1...-3....0....3...-1....1...-1...-3....2
%e A199836 .-1....1....3...-1...-1...-3...-1...-2....1...-1....2....2...-2...-1...-2....1
%e A199836 .-1...-3....3....3....3...-3...-2....0...-2...-3....0....1....1...-2....1...-2
%e A199836 ..2...-3...-2...-1....3....0....3...-1....3....2...-2....2....1....1....2...-3
%e A199836 ..1....1...-1....0...-2....3...-1....0....1....1....1....1....0...-2....0....0
%e A199836 ..0....3...-2....1....0...-1...-2....1....1....0...-2...-3...-1....3....3....2
%Y A199836 Cf. A199832.
%K A199836 nonn
%O A199836 1,1
%A A199836 _R. H. Hardin_, Nov 11 2011