A200038 T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with sum zero and with zeroth through n-1st differences all nonzero.

0, 0, 2, 0, 4, 0, 0, 6, 2, 2, 0, 8, 14, 28, 0, 0, 10, 28, 84, 26, 2, 0, 12, 52, 218, 264, 168, 0, 0, 14, 78, 444, 1074, 1450, 214, 2, 0, 16, 114, 808, 3054, 7384, 5268, 1140, 0, 0, 18, 152, 1330, 7104, 25814, 41228, 25070, 1882, 2, 0, 20, 200, 2068, 14156, 72220, 192280

Offset

1,3

Comments

Table starts

.0....0......0.......0........0.........0.........0.........0.........0

.2....4......6.......8.......10........12........14........16........18

.0....2.....14......28.......52........78.......114.......152.......200

.2...28.....84.....218......444.......808......1330......2068......2996

.0...26....264....1074.....3054......7104.....14156.....25546.....42928

.2..168...1450....7384....25814.....72220....169170....351964....667998

.0..214...5268...41228...192280....674234...1882238...4559584...9869410

.2.1140..25070..262004..1557104...6674940..22017152..61742902.151999794

.0.1882.102854.1565836.12157838..64642466.254776338.828832824

.2.7930.460146.9730070.97030120.635825548

Links

R. H. Hardin, Table of n, a(n) for n = 1..129

Example

Some solutions for n=7 k=6
.-3....1...-6...-6...-3....1...-6....4...-6...-3....4...-3....4....1....1...-6
.-6...-3....1...-2....4...-3....4...-3....1....4....5....1...-3....5...-5....2
..2....2....5....5...-2....5...-3...-1....3....3...-6...-1...-4...-6....4...-6
..4...-2....3...-3...-4...-3...-1...-6...-1...-3...-3....6...-1....4....3....5
.-2....6...-4....3....4....4....5....4....4....2....5...-1...-2...-1...-6....2
..3....1...-2....1....3...-6...-2...-2....2...-6...-1....1....1...-4....4....5
..2...-5....3....2...-2....2....3....4...-3....3...-4...-3....5....1...-1...-2

Crossrefs

Sequence in context: A258701 A246160 A081120 * A249093 A102392 A227311

Adjacent sequences: A200035 A200036 A200037 * A200039 A200040 A200041

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 12 2011

Status

approved