A188333 T(n,k)=Number of nondecreasing arrangements of n nonzero numbers in -(n+k-2)..(n+k-2) with sum zero.

0, 0, 1, 0, 2, 2, 0, 3, 4, 10, 0, 4, 8, 20, 40, 0, 5, 12, 37, 86, 197, 0, 6, 18, 61, 166, 424, 980, 0, 7, 24, 94, 288, 828, 2128, 5142, 0, 8, 32, 136, 472, 1488, 4238, 11200, 27632, 0, 9, 40, 191, 726, 2519, 7836, 22563, 60372, 152191, 0, 10, 50, 257, 1076, 4050, 13694, 42593

Offset: 1

Author

R. H. Hardin Mar 28 2011

Keywords

• nonn
• tabl

Comments

Table starts

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

......1......2......3.......4.......5.......6.......7........8........9

......2......4......8......12......18......24......32.......40.......50

.....10.....20.....37......61......94.....136.....191......257......338

.....40.....86....166.....288.....472.....726....1076.....1534.....2130

....197....424....828....1488....2519....4050....6252.....9314....13479

....980...2128...4238....7836...13694...22786...36454....56314....84496

...5142..11200..22563...42593...76251..130453..214784...341988...528926

..27632..60372.122986..236130..431488..755434.1274786..2082546..3306612

.152191.333254.684809.1333130.2477726.4423012.7621670.12729304.20676601

Examples

			Some solutions for n=8 k=6
.-8...-9..-12..-11..-12...-9...-9...-6..-11...-8..-12..-12..-12...-9..-11...-9
.-5...-7...-7...-7...-5...-6...-8...-6...-7...-7...-6..-12..-10...-6..-10...-7
.-1...-6....1...-4...-2...-3...-3...-6...-4...-4...-4...-1...-6...-2...-4...-1
.-1....1....1...-4...-2...-3....3...-5...-4....1...-4....2....4....1...-4...-1
.-1....1....2....3...-2....2....3...-5....5....1....1....4....4....1....4....1
..3....2....3....6....4....4....3....5....6....3....2....4....5....3....6....5
..3....9....5....8....8....7....4...11....6....4...11....4....6....5....9....6
.10....9....7....9...11....8....7...12....9...10...12...11....9....7...10....6
		

Links

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

Crossrefs

Row 3 is A007590(n+1)