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 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. 14
 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). Sequence in context: A267471 A268457 A244940 * A250351 A269690 A269494 Adjacent sequences: A244829 A244830 A244831 * A244833 A244834 A244835 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Jul 06 2014 STATUS approved

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Last modified March 20 15:35 EDT 2023. Contains 361384 sequences. (Running on oeis4.)