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A244788
T(n,k)=Number of length n 0..k arrays with each partial sum starting from the beginning no more than one standard deviation from its mean.
15
2, 1, 2, 2, 3, 4, 3, 6, 7, 8, 4, 13, 20, 17, 12, 5, 18, 51, 72, 41, 24, 4, 23, 88, 201, 268, 123, 36, 5, 26, 135, 454, 941, 876, 345, 72, 6, 33, 166, 851, 2424, 4153, 3236, 953, 144, 7, 48, 243, 1116, 5101, 13270, 18143, 12284, 2613, 252, 6, 57, 382, 1919, 7730, 30359, 73988
OFFSET
1,1
COMMENTS
Table starts
...2....1......2.......3........4........5.........4.........5..........6
...2....3......6......13.......18.......23........26........33.........48
...4....7.....20......51.......88......135.......166.......243........382
...8...17.....72.....201......454......851......1116......1919.......3162
..12...41....268.....941.....2424.....5101......7730.....14519......26882
..24..123....876....4153....13270....30359.....54842....118709.....249138
..36..345...3236...18143....73988...197949....396488....940083....2280068
..72..953..12284...87353...384360..1246529...2909656...7875465...21006940
.144.2613..42396..405423..2126012..8310879..21610932..64293499..195017988
.252.7149.159876.1865359.11983288.53948531.162100016.547533077.1823805952
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<=j*var36(k) for all j=1..n
LINKS
EXAMPLE
Some solutions for n=10 k=4
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..2....3....2....3....2....3....3....3....4....3....4....3....2....2....4....4
..4....4....4....2....3....2....3....3....1....4....0....1....4....4....3....1
..3....3....2....3....2....1....1....3....1....3....3....4....2....2....1....2
..2....0....3....1....3....4....2....4....4....0....3....2....3....1....1....3
..4....4....3....2....4....3....4....2....0....0....1....4....3....4....4....0
..0....4....4....1....0....0....1....1....1....2....1....2....0....4....1....0
..4....1....0....3....0....0....2....4....3....3....3....4....3....0....4....4
..3....0....0....3....1....4....4....0....3....2....1....2....1....4....3....3
CROSSREFS
Sequence in context: A225502 A152227 A246583 * A078660 A239239 A241701
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 06 2014
STATUS
approved