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%I #5 Nov 16 2016 12:30:08
%S 2,3,4,4,9,8,5,14,25,14,6,23,52,69,28,7,34,111,198,207,56,8,43,190,
%T 517,764,603,104,9,58,295,1076,2529,2976,1741,208,10,75,444,1939,6370,
%U 12497,11668,5223,416,11,94,631,3358,13139,37364,60773,45960,15445,796,12,109
%N T(n,k)=Number of length n 0..k arrays with each partial sum starting from the beginning no more than sqrt(3) standard deviations from its mean
%C Table starts
%C ...2.....3......4.......5........6.........7.........8..........9.........10
%C ...4.....9.....14......23.......34........43........58.........75.........94
%C ...8....25.....52.....111......190.......295.......444........631........896
%C ..14....69....198.....517.....1076......1939......3358.......5405.......8450
%C ..28...207....764....2529.....6370.....13139.....26256......47837......81956
%C ..56...603...2976...12497....37364.....89937....203496.....414005.....802938
%C .104..1741..11668...60773...219382....619567...1606524....3633503....7812680
%C .208..5223..45960..293467..1290578...4214681..12610616...32062641...76978472
%C .416.15445.181652.1452027..7608118..29077603..98974880..284037099..754859772
%C .796.45423.719784.7098491.44939408.198628937.777361848.2523617923.7399299882
%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<=3*j*var36(k) for all j=1..n
%H R. H. Hardin, <a href="/A244940/b244940.txt">Table of n, a(n) for n = 1..9999</a>
%e Some solutions for n=6 k=4
%e ..4....1....2....0....4....3....3....0....1....1....3....1....0....4....3....4
%e ..1....3....1....4....0....0....1....3....3....0....4....4....4....1....3....1
%e ..3....1....0....2....4....4....4....2....3....3....3....0....2....2....0....1
%e ..3....3....4....3....3....2....4....1....1....2....2....4....4....1....3....4
%e ..4....1....1....2....3....4....0....1....1....2....3....4....3....0....0....0
%e ..3....3....0....4....3....3....0....0....1....3....0....4....2....1....3....4
%Y Row 1 is A000027(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jul 08 2014
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