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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
2, 3, 4, 4, 9, 8, 5, 16, 25, 16, 6, 25, 62, 75, 30, 7, 34, 117, 242, 219, 60, 8, 47, 200, 573, 950, 657, 120, 9, 62, 315, 1162, 2833, 3744, 1947, 230, 10, 79, 482, 2187, 6916, 13785, 14802, 5737, 460, 11, 98, 679, 3792, 14859, 40894, 68311, 58662, 16835, 920, 12, 115
OFFSET
1,1
COMMENTS
Table starts
...2.....3......4.......5........6.........7.........8..........9.........10
...4.....9.....16......25.......34........47........62.........79.........98
...8....25.....62.....117......200.......315.......482........679........948
..16....75....242.....573.....1162......2187......3792.......6015.......9262
..30...219....950....2833.....6916.....14859.....29588......53105......91096
..60...657...3744...13785....40894....102301....234128.....469965.....899962
.120..1947..14802...68311...241778....707567...1843104....4169823....8845276
.230..5737..58662..339839..1430672...4909019..14502774...37082231...87596238
.460.16835.232916.1677913..8475456..34131599.115222470..330409737..864410260
.920.50505.926120.8250991.50269530.235879457.912575878.2948726733.8580746182
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.
LINKS
EXAMPLE
Some solutions for n=6 k=4
..2....3....0....4....3....2....3....0....4....1....4....0....4....0....1....3
..4....4....4....2....2....1....4....3....3....3....3....4....3....2....0....2
..3....1....4....1....1....3....0....1....0....0....3....0....1....3....1....4
..0....2....3....4....2....2....1....4....2....1....3....1....0....3....1....1
..2....1....1....0....2....1....1....2....4....2....3....0....2....3....3....3
..3....1....2....3....2....2....1....4....2....0....0....4....1....1....0....0
CROSSREFS
Row 1 is A000027(n+1).
Sequence in context: A267471 A268457 A244940 * A250351 A269690 A269494
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 06 2014
STATUS
approved