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%I #5 Nov 16 2016 12:30:07
%S 2,3,4,4,7,6,5,14,21,12,4,19,52,59,24,5,22,89,198,163,42,6,33,118,431,
%T 764,447,84,7,42,199,646,2009,2740,1341,168,8,57,316,1299,3602,9257,
%U 10484,3905,312,9,68,469,2336,8695,20358,45207,40696,11271,624,10,87,624
%N T(n,k)=Number of length n 0..k arrays with each partial sum starting from the beginning no more than sqrt(2) standard deviations from its mean
%C Table starts
%C ...2.....3......4.......5........4.........5.........6..........7..........8
%C ...4.....7.....14......19.......22........33........42.........57.........68
%C ...6....21.....52......89......118.......199.......316........469........624
%C ..12....59....198.....431......646......1299......2336.......3949.......5912
%C ..24...163....764....2009.....3602......8695.....17392......33803......55282
%C ..42...447...2740....9257....20358.....56609....130548.....282785.....518428
%C ..84..1341..10484...45207...116272....382743...1019188....2438447....5021116
%C .168..3905..40696..215411...669516...2617609...7890336...21257775...48258938
%C .312.11271.159332.1061375..3880216..17614513..61161968..182555691..464345786
%C .624.32357.627156.5141999.22605350.117799671.475132844.1597877557.4477346412
%C Computation in integer form, using 6 times the 0..k mean and 36 times the variance, mean6(k)=3*k; var36(k)=6*k*(2*k+1)-mean6(k)^2; then (6*sum{x(i),i=1..j}-j*mean6(k))^2<=2*j*var36(k) for all j=1..n
%H R. H. Hardin, <a href="/A244903/b244903.txt">Table of n, a(n) for n = 1..9999</a>
%e Some solutions for n=6 k=4
%e ..4....1....4....4....4....1....3....1....3....3....2....3....2....3....2....4
%e ..0....1....1....1....1....4....2....4....1....3....3....1....1....3....0....1
%e ..2....4....0....1....1....1....3....1....1....0....2....0....3....0....4....3
%e ..2....2....0....0....4....0....0....4....4....2....0....3....1....3....4....2
%e ..2....4....4....3....4....4....3....2....3....1....4....0....1....0....4....3
%e ..3....0....0....3....2....1....3....1....0....3....4....2....1....3....1....3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jul 07 2014
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