A203291 T(n,k)=Number of arrays of 2n nondecreasing integers in -k..k with sum zero and equal numbers greater than zero and less than zero

2, 3, 3, 4, 6, 4, 5, 12, 10, 5, 6, 21, 28, 15, 6, 7, 35, 69, 57, 21, 7, 8, 54, 154, 188, 104, 28, 8, 9, 80, 310, 544, 444, 176, 36, 9, 10, 113, 580, 1380, 1614, 944, 280, 45, 10, 11, 155, 1013, 3172, 5036, 4206, 1844, 425, 55, 11, 12, 206, 1680, 6687, 13934, 15798, 9880

Offset

1,1

Comments

Table starts

..2..3...4....5.....6......7.......8........9.......10........11........12

..3..6..12...21....35.....54......80......113......155.......206.......268

..4.10..28...69...154....310.....580.....1013.....1680......2662......4064

..5.15..57..188...544...1380....3172.....6687....13163.....24435.....43195

..6.21.104..444..1614...5036...13934....34847....80258....172405....349182

..7.28.176..944..4206..15798...51768...151393...403131....991692...2280620

..8.36.280.1844..9880..43958..168314...568933..1734054...4842044..12545910

..9.45.425.3369.21363.111053..491187..1899856..6570506..20665432..59915342

.10.55.620.5825.43136.259023.1310474..5750208.22393894..78796188.254083954

.11.66.876.9621.82267.565010.3241912.16015498.69763326.272964800.973625950

Links

R. H. Hardin, Table of n, a(n) for n = 1..1921

Example

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

Crossrefs

Column 2 is A000217(n+1)

Sequence in context: A014410 A180986 A200763 * A220053 A320509 A358298

Adjacent sequences: A203288 A203289 A203290 * A203292 A203293 A203294

Keyword

nonn,tabl

Author

R. H. Hardin Dec 31 2011

Status

approved