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 A244832 T(n,k) = Number of length n 0..k arrays with each partial sum starting from the beginning no more than two standard deviations from its mean. 14

%I #9 Oct 01 2021 17:32:43

%S 2,3,4,4,9,8,5,16,25,16,6,25,62,75,30,7,34,117,242,219,60,8,47,200,

%T 573,950,657,120,9,62,315,1162,2833,3744,1947,230,10,79,482,2187,6916,

%U 13785,14802,5737,460,11,98,679,3792,14859,40894,68311,58662,16835,920,12,115

%N T(n,k) = Number of length n 0..k arrays with each partial sum starting from the beginning no more than two standard deviations from its mean.

%C Table starts

%C ...2.....3......4.......5........6.........7.........8..........9.........10

%C ...4.....9.....16......25.......34........47........62.........79.........98

%C ...8....25.....62.....117......200.......315.......482........679........948

%C ..16....75....242.....573.....1162......2187......3792.......6015.......9262

%C ..30...219....950....2833.....6916.....14859.....29588......53105......91096

%C ..60...657...3744...13785....40894....102301....234128.....469965.....899962

%C .120..1947..14802...68311...241778....707567...1843104....4169823....8845276

%C .230..5737..58662..339839..1430672...4909019..14502774...37082231...87596238

%C .460.16835.232916.1677913..8475456..34131599.115222470..330409737..864410260

%C .920.50505.926120.8250991.50269530.235879457.912575878.2948726733.8580746182

%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<=4*j*var36(k) for all j=1..n.

%H R. H. Hardin, <a href="/A244832/b244832.txt">Table of n, a(n) for n = 1..9999</a>

%e Some solutions for n=6 k=4

%e ..2....3....0....4....3....2....3....0....4....1....4....0....4....0....1....3

%e ..4....4....4....2....2....1....4....3....3....3....3....4....3....2....0....2

%e ..3....1....4....1....1....3....0....1....0....0....3....0....1....3....1....4

%e ..0....2....3....4....2....2....1....4....2....1....3....1....0....3....1....1

%e ..2....1....1....0....2....1....1....2....4....2....3....0....2....3....3....3

%e ..3....1....2....3....2....2....1....4....2....0....0....4....1....1....0....0

%Y Row 1 is A000027(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jul 06 2014

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Last modified October 4 02:45 EDT 2023. Contains 365872 sequences. (Running on oeis4.)