A199837 - OEIS

%I #8 May 16 2018 11:19:31

%S 34,6126,113884,888420,4340094,15805218,47040968,120843752,277500282,

%T 583380598,1141982292,2107735180,3702875670,6237700074,10134506112,

%U 15955531856,24435201362,36516986238,53395192396,76561981236

%N Number of -n..n arrays x(0..7) of 8 elements with zero sum and no two neighbors summing to zero.

%C Row 6 of A199832.

%H R. H. Hardin, <a href="/A199837/b199837.txt">Table of n, a(n) for n = 1..197</a>

%F Empirical: a(n) = (19328/315)*n^7 - (1424/45)*n^6 + (704/45)*n^5 - (112/9)*n^4 - (124/45)*n^3 + (229/45)*n^2 - (131/105)*n.

%F Conjectures from _Colin Barker_, May 16 2018: (Start)

%F G.f.: 2*x*(17 + 2927*x + 32914*x^2 + 73486*x^3 + 40405*x^4 + 4819*x^5 + 56*x^6) / (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=3:

%e ..0....1....2....2...-2....0...-2....0...-2....2....1...-2...-1...-3....0...-2

%e ..2....0....0....1...-1....2...-1....1....0....1....3....1....2....0...-2....3

%e ..2...-3....1....0....0...-3....0....2....2....2....0....0....1....3....3....0

%e .-3....0...-3...-2...-1...-1....1...-3...-3....0....1....2...-2....0....2....1

%e ..0....1....0...-2....0....0....1...-1...-1...-3...-3....2...-1...-1...-1....2

%e ..3...-3...-1....3....1....1....0...-1....3...-1...-1....0....0....0...-1....0

%e .-2....2...-2....0....2....2....2....0....3...-3...-3...-1....3....1....0...-2

%e .-2....2....3...-2....1...-1...-1....2...-2....2....2...-2...-2....0...-1...-2

%Y Cf. A199832.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 11 2011