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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 August 5 05:34 EDT 2024. Contains 374935 sequences. (Running on oeis4.)