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%I #4 Jun 06 2015 08:40:47
%S 1,2,2,3,6,4,4,12,18,8,5,20,45,50,16,6,28,80,130,105,27,7,36,125,264,
%T 331,181,33,8,46,179,511,809,834,316,35,9,56,257,830,2094,2506,2115,
%U 560,45,9,67,345,1408,4021,9099,8432,5726,969,60,10,73,468,2150,8116,20462,40789
%N T(n,k)=Number of length n 1..(k+1) arrays with every leading partial sum divisible by 2, 3, 5 or 7
%C Table starts
%C ..1....2.....3......4.......5........6........7.........8.........9..........9
%C ..2....6....12.....20......28.......36.......46........56........67.........73
%C ..4...18....45.....80.....125......179......257.......345.......468........560
%C ..8...50...130....264.....511......830.....1408......2150......3370.......4440
%C .16..105...331....809....2094.....4021.....8116.....14058.....25047......35962
%C .27..181...834...2506....9099....20462....48479.....93595....186047.....290231
%C .33..316..2115...8432...40789...105719...290231....615072...1376125....2357746
%C .35..560..5726..30362..182685...546640..1702510...4010997..10317196...19499390
%C .45..969.16873.109520..818100..2789557..9898375..26612118..78604973..162595685
%C .60.1777.50003.391836.3633049.14124297.58647747.180705283.600180109.1349514483
%H R. H. Hardin, <a href="/A258631/b258631.txt">Table of n, a(n) for n = 1..9999</a>
%e Some solutions for n=8 k=4
%e ..3....4....3....5....5....2....3....5....4....3....3....4....4....3....4....3
%e ..5....4....2....5....2....1....2....4....2....4....5....2....1....1....5....5
%e ..1....4....3....4....1....4....2....3....1....3....2....1....3....1....5....2
%e ..1....2....4....1....4....3....3....3....5....5....2....5....2....2....4....4
%e ..4....4....4....1....2....4....4....5....3....5....3....4....5....1....3....2
%e ..4....2....2....4....4....4....4....5....3....1....1....5....1....2....1....4
%e ..3....2....2....5....2....2....4....2....3....1....2....3....2....4....5....2
%e ..5....3....4....2....5....4....5....1....4....5....3....3....2....4....3....4
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jun 06 2015
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