A199837 Number of -n..n arrays x(0..7) of 8 elements with zero sum and no two neighbors summing to zero.

34, 6126, 113884, 888420, 4340094, 15805218, 47040968, 120843752, 277500282, 583380598, 1141982292, 2107735180, 3702875670, 6237700074, 10134506112, 15955531856, 24435201362, 36516986238, 53395192396, 76561981236

Offset: 1

Author

R. H. Hardin, Nov 11 2011

Keywords

• nonn

Comments

Row 6 of A199832.

Examples

			Some solutions for n=3:
..0....1....2....2...-2....0...-2....0...-2....2....1...-2...-1...-3....0...-2
..2....0....0....1...-1....2...-1....1....0....1....3....1....2....0...-2....3
..2...-3....1....0....0...-3....0....2....2....2....0....0....1....3....3....0
.-3....0...-3...-2...-1...-1....1...-3...-3....0....1....2...-2....0....2....1
..0....1....0...-2....0....0....1...-1...-1...-3...-3....2...-1...-1...-1....2
..3...-3...-1....3....1....1....0...-1....3...-1...-1....0....0....0...-1....0
.-2....2...-2....0....2....2....2....0....3...-3...-3...-1....3....1....0...-2
.-2....2....3...-2....1...-1...-1....2...-2....2....2...-2...-2....0...-1...-2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..197

Crossrefs

Cf. A199832.

Formula

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.

Conjectures from Colin Barker, May 16 2018: (Start)

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.

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.

(End)