

A345318


Median absolute deviation of {2*k^2  k=1..n}.


1



0, 3, 6, 8, 14, 20, 24, 32, 42, 48, 56, 72, 80, 91, 110, 120, 130, 153, 168, 180, 208, 224, 238, 264, 288, 304, 330, 360, 378, 405, 440, 460, 480, 527, 550, 576, 624, 648, 672, 720, 754, 780, 832, 868, 896, 943, 990, 1020, 1062, 1120, 1152, 1196, 1258, 1292, 1326, 1400
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OFFSET

1,2


COMMENTS

The factor 2 in 2*k^2 in the definition is to ensure that median and median absolute deviation are always integers.
Conjecture: a(n) ~ (sqrt(3)/4) * n^2.
The conjecture is true. See links.  Sela Fried, Jul 17 2024.


LINKS



EXAMPLE

For n = 5 the sample is {2*k^2  k=1..5} = {2, 8, 18, 32, 50}, its median is 18, the absolute deviations from the median are {16, 10, 0, 14, 32}, the median of the absolute deviations is 14, so a(5) = 14.
For n = 6 the sample is {2*k^2  k=1..6} = {2, 8, 18, 32, 50, 72}, its median is (18+32)/2 = 25, the absolute deviations from the median are {23, 17, 7, 7, 25, 47}, the median of the absolute deviations is (17+23)/2 = 20, so a(6) = 20.


MATHEMATICA

Table[MedianDeviation[Table[2 k^2, {k, n}]], {n, 56}]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



