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

Author

R. H. Hardin Mar 24 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

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)