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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
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 07 2014
STATUS
approved