Linear programming square root times constant

(*start*)
a = 1;
b = 0;
nn = 200;
Monitor[TableForm[
   L2 = 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}, {-a*(n - 1), a + b*(n - 1)}], {n, 1,
        k}]], {k, 1, nn}]];, k]
t1 = Table[Sum[If[L2[[n, k]] <= -1, 1, 0], {k, 2, n}], {n, 2, nn}]
t2 = Table[Round[-1 + Sqrt[2]*Sqrt[((1 + a)*(-1 + n))/a]], {n, 2, nn}]
Show[ListLinePlot[t1, PlotStyle -> Red], ListLinePlot[t2]]
t1 - t2
Count[%, 0] + 1
(*end*)


(*version 2, 3.5.2020*)

(*start*)a = 1;
b = 0;
nn = 200;
Monitor[TableForm[
   L2 = 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}, {-a*(n - 1), a + b*(n - 1)}], {n, 1,
        k}]], {k, 1, nn}]];, k]
t1 = Table[Sum[If[L2[[n, k]] <= -1, 1, 0], {k, 2, n}], {n, 2, nn}]
t2 = Table[Round[-1 + 2 Sqrt[-1 + n]], {n, 2, nn}]
Show[ListLinePlot[t1, PlotStyle -> Red], ListLinePlot[t2]]
t1 - t2
Count[%, 0] + 1
(*end*)