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%I #5 Mar 31 2012 12:36:37
%S 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,
%T 153,1,8,32,103,239,428,575,376,1,9,41,149,399,845,1393,1739,931,1,10,
%U 50,206,630,1532,2958,4561,5307,2317,1,11,61,276,944,2600,5754,10349,15032
%N 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
%C Table starts
%C ....1.....1.....1......1......1......1.......1.......1.......1.......1........1
%C ....2.....3.....4......5......6......7.......8.......9......10......11.......12
%C ....5.....8....13.....18.....25.....32......41......50......61......72.......85
%C ...11....23....42.....68....103....149.....206.....276.....361.....461......578
%C ...26....66...132....239....399....630.....944....1367....1913....2612.....3482
%C ...63...192...428....845...1532...2600....4188....6465....9634...13932....19636
%C ..153...575..1393...2958...5754..10426...17879...29268...46126...70322...104253
%C ..376..1739..4561..10349..21383..41079...74424..128462..212862..340592...528705
%C ..931..5307.15032..36111..78735.159330..303400..549404..953172.1594101..2581937
%C .2317.16304.49889.126121.288580.611698.1218440.2304210.4169150.7260993.12230924
%H R. H. Hardin, <a href="/A199847/b199847.txt">Table of n, a(n) for n = 1..958</a>
%e Some solutions for n=7 k=6
%e ..5....4....2....2....6....5....2...-1....3....3....6....4....6....6....5....3
%e ..4....2....1....3....6....2....1....0....3....1....3....1....6....1....5...-1
%e ..1....2....1....3....0....3....1....1...-1....1....4....1...-2....1...-1...-1
%e ..0...-1...-1....0...-4...-2....1....0....0...-1....1....2...-2....1...-3....0
%e .-2....0...-2...-1...-3...-3....1....1....1...-1...-2....2...-2....0...-3...-1
%e .-2...-1...-1...-1...-2...-3....0....0....0....0...-6...-5...-3...-3...-2....0
%e .-6...-6....0...-6...-3...-2...-6...-1...-6...-3...-6...-5...-3...-6...-1....0
%Y Column 1 is A051286
%Y Row 3 is A000982(n+2)
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Nov 11 2011
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