A188211 T(n,k)=Number of nondecreasing arrangements of n numbers in -(n+k-2)..(n+k-2) with sum zero.

1, 1, 2, 1, 3, 5, 1, 4, 8, 18, 1, 5, 13, 33, 73, 1, 6, 18, 55, 141, 338, 1, 7, 25, 86, 252, 676, 1656, 1, 8, 32, 126, 414, 1242, 3370, 8512, 1, 9, 41, 177, 649, 2137, 6375, 17575, 45207, 1, 10, 50, 241, 967, 3486, 11322, 33885, 94257, 246448, 1, 11, 61, 318, 1394, 5444

Offset

1,3

Comments

Table starts

......1......1.......1.......1.......1.......1........1........1........1

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

......5......8......13......18......25......32.......41.......50.......61

.....18.....33......55......86.....126.....177......241......318......410

.....73....141.....252.....414.....649.....967.....1394.....1944.....2649

....338....676....1242....2137....3486....5444.....8196....11963....17002

...1656...3370....6375...11322...19138...30982....48417....73316...108108

...8512..17575...33885...61731..107233..178870...288100...450096...684572

..45207..94257..184717..343363..610358.1043534..1724882..2767118..4323349

.246448.517971.1028172.1943488.3521260.6147894.10388788.17052653.27273240

Links

R. H. Hardin, Table of n, a(n) for n = 1..430

Example

Some solutions for n=5 k=3
.-5...-5...-4...-4...-6...-3...-6...-4...-2...-6...-2...-6...-4...-5...-5...-4
.-2...-1...-4...-2...-5...-3...-1...-3...-1...-6...-1...-1...-3...-4...-3...-4
..0....0...-1...-2...-1...-1....0...-1...-1....1...-1....0....1...-1....0....1
..1....0....3....3....6....2....2....3....1....5....0....1....1....5....4....3
..6....6....6....5....6....5....5....5....3....6....4....6....5....5....4....4

Crossrefs

Column 1 is A039744

Column 2 is A109655

Row 3 is A000982(n+2)

Row 5 is A188183(n+2)

Row 7 is A188185(n+3)

Sequence in context: A117584 A199847 A047997 * A175009 A297395 A297595

Adjacent sequences: A188208 A188209 A188210 * A188212 A188213 A188214

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 24 2011

Status

approved