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

Author

R. H. Hardin, Jul 06 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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