|
| |
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
R. H. Hardin, Table of n, a(n) for n = 1..9999
|
|
|
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
Adjacent sequences: A244829 A244830 A244831 * A244833 A244834 A244835
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
R. H. Hardin, Jul 06 2014
|
|
|
STATUS
|
approved
|
| |
|
|
