Gary OEIS recurrence

(*program 1 start*)Clear[nn, t, n, k, c];
nn = 60;
c = 0;
t[n_, 1] = If[n >= 1, n, 0];
t[1, k_] = If[k >= 1, k, 0];
t[n_, k_] :=
  t[n, k] =
   If[And[n > 1, k > 1],
    If[n > k, t[n, k - 1] - t[n - k, k - 1] + t[n - k + c, k],
     t[k, n - 1] - t[k - n, n - 1] + t[k - n + c, n]], 0];
TableForm[Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}]];
a = Flatten[Table[t[n, n], {n, 1, nn}]]
Differences[%]
ListLinePlot[a]
 (*=Dirichlet inverse of Euler totient*)
(*program 1 end*)

(*program 2 start*)
Clear[nn, t, n, k, c];
nn = 60;
c = 1;
t[n_, 1] = If[n >= 1, n, 0];
t[1, k_] = If[k >= 1, k, 0];
t[n_, k_] :=
  t[n, k] =
   If[And[n > 1, k > 1],
    If[n > k, t[n, k - 1] - t[n - k, k - 1] + t[n - k + c, k],
     t[k, n - 1] - t[k - n, n - 1] + t[k - n + c, n]], 0];
TableForm[Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}]];
b = Table[t[n, n], {n, 1, nn}]
ListLinePlot[b]
Differences[b]
(*=The square numbers*)
(*program 2 end*)