A244940 - OEIS

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A244940

T(n,k)=Number of length n 0..k arrays with each partial sum starting from the beginning no more than sqrt(3) standard deviations from its mean

2, 3, 4, 4, 9, 8, 5, 14, 25, 14, 6, 23, 52, 69, 28, 7, 34, 111, 198, 207, 56, 8, 43, 190, 517, 764, 603, 104, 9, 58, 295, 1076, 2529, 2976, 1741, 208, 10, 75, 444, 1939, 6370, 12497, 11668, 5223, 416, 11, 94, 631, 3358, 13139, 37364, 60773, 45960, 15445, 796, 12, 109

(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.....14......23.......34........43........58.........75.........94

...8....25.....52.....111......190.......295.......444........631........896

..14....69....198.....517.....1076......1939......3358.......5405.......8450

..28...207....764....2529.....6370.....13139.....26256......47837......81956

..56...603...2976...12497....37364.....89937....203496.....414005.....802938

.104..1741..11668...60773...219382....619567...1606524....3633503....7812680

.208..5223..45960..293467..1290578...4214681..12610616...32062641...76978472

.416.15445.181652.1452027..7608118..29077603..98974880..284037099..754859772

.796.45423.719784.7098491.44939408.198628937.777361848.2523617923.7399299882

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<=3*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

..4....1....2....0....4....3....3....0....1....1....3....1....0....4....3....4

..1....3....1....4....0....0....1....3....3....0....4....4....4....1....3....1

..3....1....0....2....4....4....4....2....3....3....3....0....2....2....0....1

..3....3....4....3....3....2....4....1....1....2....2....4....4....1....3....4

..4....1....1....2....3....4....0....1....1....2....3....4....3....0....0....0

..3....3....0....4....3....3....0....0....1....3....0....4....2....1....3....4

CROSSREFS

Row 1 is A000027(n+1)