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

1,1

Comments

Row 6 of A199832.

Links

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

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)

Example

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

Crossrefs

Cf. A199832.

Sequence in context: A291976 A212035 A292750 * A267916 A005334 A033511

Adjacent sequences: A199834 A199835 A199836 * A199838 A199839 A199840

Keyword

nonn

Author

R. H. Hardin, Nov 11 2011

Status

approved