---------------------------
(*start*)
nn = 42;
TableForm[
L1 = Table[
LinearProgramming[
Table[1/n, {n, 1, k}], {Table[If[n == 1, k, 1], {n, 1, k}]}, {{1,
0}}, Table[
If[n == 1, {-1, 1}, {-2 (n - 1), 2 (n - 1)}], {n, 1, k}]], {k,
1, nn}]];
b = Table[Sum[-Sign[-1 + Sign[L1[[n, k]]]], {k, 1, n}], {n, 1, nn}]
Table[Floor[n/Sqrt[2]], {n, 1, nn}]
%% - %
(*end*)
{0, 1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, \
14, 15, 16, 16, 17, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, \
26, 27, 28, 28, 29}