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A244940
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
14
2, 3, 4, 4, 9, 8, 5, 14, 25, 14, 6, 23, 52, 69, 28, 7, 34, 111, 198, 207, 56, 8, 43, 190, 517, 764, 603, 104, 9, 58, 295, 1076, 2529, 2976, 1741, 208, 10, 75, 444, 1939, 6370, 12497, 11668, 5223, 416, 11, 94, 631, 3358, 13139, 37364, 60773, 45960, 15445, 796, 12, 109
OFFSET
1,1
COMMENTS
Table starts
...2.....3......4.......5........6.........7.........8..........9.........10
...4.....9.....14......23.......34........43........58.........75.........94
...8....25.....52.....111......190.......295.......444........631........896
..14....69....198.....517.....1076......1939......3358.......5405.......8450
..28...207....764....2529.....6370.....13139.....26256......47837......81956
..56...603...2976...12497....37364.....89937....203496.....414005.....802938
.104..1741..11668...60773...219382....619567...1606524....3633503....7812680
.208..5223..45960..293467..1290578...4214681..12610616...32062641...76978472
.416.15445.181652.1452027..7608118..29077603..98974880..284037099..754859772
.796.45423.719784.7098491.44939408.198628937.777361848.2523617923.7399299882
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
LINKS
EXAMPLE
Some solutions for n=6 k=4
..4....1....2....0....4....3....3....0....1....1....3....1....0....4....3....4
..1....3....1....4....0....0....1....3....3....0....4....4....4....1....3....1
..3....1....0....2....4....4....4....2....3....3....3....0....2....2....0....1
..3....3....4....3....3....2....4....1....1....2....2....4....4....1....3....4
..4....1....1....2....3....4....0....1....1....2....3....4....3....0....0....0
..3....3....0....4....3....3....0....0....1....3....0....4....2....1....3....4
CROSSREFS
Row 1 is A000027(n+1)
Sequence in context: A228461 A267471 A268457 * A244832 A250351 A269690
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 08 2014
STATUS
approved