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.

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

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