A244832 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

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).