A345318 Median absolute deviation of {2*k^2 | k=1..n}.

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

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

Table of n, a(n) for n=1..56.

Sela Fried, Median absolute deviation, 2024.

Sela Fried, Proofs of some Conjectures from the OEIS, arXiv:2410.07237 [math.NT], 2024. See p. 3.

Wikipedia, Median absolute deviation

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

Cf. A001105 (doubled squares), A000982 (their medians).

Sequence in context: A352319 A297211 A365314 * A274605 A213983 A174133

Adjacent sequences: A345315 A345316 A345317 * A345319 A345320 A345321

Keyword

nonn,easy

Author

Vladimir Reshetnikov, Jun 13 2021

Status

approved