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%I #8 Aug 14 2018 08:57:45
%S 255,7425,73983,419841,1690623,5407233,14661375,35111681,76335103,
%T 153588225,290033151,519482625,889719039,1466441985,2337899007,
%U 3620254209,5463749375,8059712257,11648466687,16528199169,23064836607
%N Number of -n..n arrays of length 7 with the sum ahead of each element differing from the sum following that element by n or less.
%C Row 7 of A221967.
%H R. H. Hardin, <a href="/A221970/b221970.txt">Table of n, a(n) for n = 1..31</a>
%F Empirical: a(n) = (488/45)*n^7 + (1708/45)*n^6 + (2912/45)*n^5 + (602/9)*n^4 + (2072/45)*n^3 + (952/45)*n^2 + (32/5)*n + 1.
%F Conjectures from _Colin Barker_, Aug 14 2018: (Start)
%F G.f.: x*(255 + 5385*x + 21723*x^2 + 21597*x^3 + 5469*x^4 + 219*x^5 + 9*x^6 - x^7) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F (End)
%e Some solutions for n=6:
%e ..0....0....0...-6....0....0....0....0....0....0....0....0...-6....0....0....0
%e ..0....0....0....0....0...-6....0....0....0....0....0....0....0....0....0....0
%e ..6....3....2....2....1....5....3....6....4...-1...-4...-4...-4...-3...-1....4
%e .-4...-3....5....2...-1....2...-6...-6....0...-3....2....4....4....0....3...-2
%e .-4...-5...-5...-4....0...-2....6....0...-5....2....5....0...-1....1...-6...-1
%e ..3....5....0....1...-5...-5....1....4....1...-4...-4...-6....2....0....6....0
%e ..4...-2....4...-4....5....1....0...-4....3....0...-1....0...-6....2....0...-1
%Y Cf. A221967.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 01 2013
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