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A244903 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 15

%I

%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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Last modified October 24 09:09 EDT 2021. Contains 348220 sequences. (Running on oeis4.)