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

1,5

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

Links

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

Example

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

Crossrefs

Row 3 is A007590(n+1)

Sequence in context: A294598 A077264 A349344 * A283269 A201947 A098816

Adjacent sequences: A188330 A188331 A188332 * A188334 A188335 A188336

Keyword

nonn,tabl

Author

R. H. Hardin Mar 28 2011

Status

approved