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.

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

R. H. Hardin, Table of n, a(n) for n = 1..9999

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

Adjacent sequences: A244785 A244786 A244787 * A244789 A244790 A244791

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 06 2014

Status

approved