A188181 T(n,k) is the number of strictly increasing arrangements of n numbers in -(n+k-2)..(n+k-2) with sum zero.

1, 1, 1, 1, 2, 2, 1, 3, 5, 5, 1, 4, 8, 12, 12, 1, 5, 13, 24, 32, 32, 1, 6, 18, 43, 73, 94, 94, 1, 7, 25, 69, 141, 227, 289, 289, 1, 8, 32, 104, 252, 480, 734, 910, 910, 1, 9, 41, 150, 414, 920, 1656, 2430, 2934, 2934, 1, 10, 50, 207, 649, 1636, 3370, 5744, 8150, 9686, 9686, 1, 11

Offset: 1

Author

R. H. Hardin, Mar 23 2011

Keywords

• nonn
• tabl

Examples

			Table starts
....1....1.....1.....1......1......1......1.......1.......1.......1.......1
....1....2.....3.....4......5......6......7.......8.......9......10......11
....2....5.....8....13.....18.....25.....32......41......50......61......72
....5...12....24....43.....69....104....150.....207.....277.....362.....462
...12...32....73...141....252....414....649.....967....1394....1944....2649
...32...94...227...480....920...1636...2739....4370....6698....9926...14293
...94..289...734..1656...3370...6375..11322...19138...30982...48417...73316
..289..910..2430..5744..12346..24591..46029...81805..139143..227930..361384
..910.2934..8150.20094..45207..94257.184717..343363..610358.1043534.1724882
.2934.9686.27718.70922.165821.360002.734517.1421530.2628824.4672836.8022362
Some solutions for n=7 and k=5:
.-7...-9...-8..-10...-6...-6...-9...-8...-8...-7...-9..-10...-9...-8...-9...-7
.-5...-7...-6...-7...-5...-5...-4...-6...-7...-3...-8...-5...-3...-7...-5...-4
.-3...-1...-5...-4...-4...-3...-1...-4...-5...-2...-6...-3...-1...-3...-4...-3
.-1....0...-1....3...-3...-2....0...-1....0...-1....4....0....1....1...-1...-1
..3....3....2....5...-1....1....1....4....3....0....5....3....3....2....4....0
..4....4....8....6....9....7....4....5....7....4....6....5....4....5....6....7
..9...10...10....7...10....8....9...10...10....9....8...10....5...10....9....8
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..550

Crossrefs

Column 1 is A076822.

Column 2 is A002838.

Cf. A000982.

Formula

T(3,n) = A000982(n+1).