A199847 T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum and no element more than one greater than the previous

1, 1, 2, 1, 3, 5, 1, 4, 8, 11, 1, 5, 13, 23, 26, 1, 6, 18, 42, 66, 63, 1, 7, 25, 68, 132, 192, 153, 1, 8, 32, 103, 239, 428, 575, 376, 1, 9, 41, 149, 399, 845, 1393, 1739, 931, 1, 10, 50, 206, 630, 1532, 2958, 4561, 5307, 2317, 1, 11, 61, 276, 944, 2600, 5754, 10349, 15032

Offset

1,3

Comments

Table starts

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

....2.....3.....4......5......6......7.......8.......9......10......11.......12

....5.....8....13.....18.....25.....32......41......50......61......72.......85

...11....23....42.....68....103....149.....206.....276.....361.....461......578

...26....66...132....239....399....630.....944....1367....1913....2612.....3482

...63...192...428....845...1532...2600....4188....6465....9634...13932....19636

..153...575..1393...2958...5754..10426...17879...29268...46126...70322...104253

..376..1739..4561..10349..21383..41079...74424..128462..212862..340592...528705

..931..5307.15032..36111..78735.159330..303400..549404..953172.1594101..2581937

.2317.16304.49889.126121.288580.611698.1218440.2304210.4169150.7260993.12230924

Links

R. H. Hardin, Table of n, a(n) for n = 1..958

Example

Some solutions for n=7 k=6
..5....4....2....2....6....5....2...-1....3....3....6....4....6....6....5....3
..4....2....1....3....6....2....1....0....3....1....3....1....6....1....5...-1
..1....2....1....3....0....3....1....1...-1....1....4....1...-2....1...-1...-1
..0...-1...-1....0...-4...-2....1....0....0...-1....1....2...-2....1...-3....0
.-2....0...-2...-1...-3...-3....1....1....1...-1...-2....2...-2....0...-3...-1
.-2...-1...-1...-1...-2...-3....0....0....0....0...-6...-5...-3...-3...-2....0
.-6...-6....0...-6...-3...-2...-6...-1...-6...-3...-6...-5...-3...-6...-1....0

Crossrefs

Column 1 is A051286

Row 3 is A000982(n+2)

Sequence in context: A119355 A076110 A117584 * A047997 A188211 A175009

Adjacent sequences: A199844 A199845 A199846 * A199848 A199849 A199850

Keyword

nonn,tabl

Author

R. H. Hardin Nov 11 2011

Status

approved