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

Author

R. H. Hardin Dec 31 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 2 is A000217(n+1)