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A244903 T(n,k)=Number of length n 0..k arrays with each partial sum starting from the beginning no more than sqrt(2) standard deviations from its mean 15
2, 3, 4, 4, 7, 6, 5, 14, 21, 12, 4, 19, 52, 59, 24, 5, 22, 89, 198, 163, 42, 6, 33, 118, 431, 764, 447, 84, 7, 42, 199, 646, 2009, 2740, 1341, 168, 8, 57, 316, 1299, 3602, 9257, 10484, 3905, 312, 9, 68, 469, 2336, 8695, 20358, 45207, 40696, 11271, 624, 10, 87, 624 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...2.....3......4.......5........4.........5.........6..........7..........8

...4.....7.....14......19.......22........33........42.........57.........68

...6....21.....52......89......118.......199.......316........469........624

..12....59....198.....431......646......1299......2336.......3949.......5912

..24...163....764....2009.....3602......8695.....17392......33803......55282

..42...447...2740....9257....20358.....56609....130548.....282785.....518428

..84..1341..10484...45207...116272....382743...1019188....2438447....5021116

.168..3905..40696..215411...669516...2617609...7890336...21257775...48258938

.312.11271.159332.1061375..3880216..17614513..61161968..182555691..464345786

.624.32357.627156.5141999.22605350.117799671.475132844.1597877557.4477346412

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<=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=6 k=4

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

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

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

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

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

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

CROSSREFS

Sequence in context: A049988 A079247 A325588 * A342337 A167932 A006087

Adjacent sequences:  A244900 A244901 A244902 * A244904 A244905 A244906

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 07 2014

STATUS

approved

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Last modified September 18 06:41 EDT 2021. Contains 347509 sequences. (Running on oeis4.)