%I #8 Aug 14 2018 08:57:38
%S 129,2305,16513,73089,241153,653185,1535745,3246337,6316417,11500545,
%T 19831681,32682625,51833601,79545985,118642177,172591617,245602945,
%U 342722305,469937793,634290049,843988993,1108536705,1438856449
%N Number of -n..n arrays of length 6 with the sum ahead of each element differing from the sum following that element by n or less.
%C Row 6 of A221967.
%H R. H. Hardin, <a href="/A221969/b221969.txt">Table of n, a(n) for n = 1..35</a>
%F Empirical: a(n) = (128/15)*n^6 + (128/5)*n^5 + (112/3)*n^4 + 32*n^3 + (272/15)*n^2 + (32/5)*n + 1.
%F Conjectures from _Colin Barker_, Aug 14 2018: (Start)
%F G.f.: x*(3 + x)*(43 + 453*x + 878*x^2 + 170*x^3 - 9*x^4 + x^5) / (1 - x)^7.
%F 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 (End)
%e Some solutions for n=6:
%e ..0...-3....0....3....3...-6....3....3...-6....0....3....0...-6...-3...-3....0
%e ..1...-5....5...-3...-3....3...-3....3....1...-2...-6...-3....5...-3....1....0
%e ..3....4...-3...-1...-5....3....5...-4....5....4...-1....5...-4....3....0....1
%e .-2...-3...-5....0....4...-2...-3....0...-5...-3....0...-3....0...-1....3...-6
%e .-4....1....5...-2....4...-1....2....2...-1....4....3...-1....2....2....0....5
%e ..4...-2....0....4...-5...-2....4....2...-4...-2...-1....2...-1...-6...-2....1
%Y Cf. A221967.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 01 2013