A051261 Main diagonal of A018219, i.e., (n, n, a_n) is a winning position.
0, 4, 6, 1, 3, 7, 11, 2, 5, 10, 17, 23, 21, 9, 28, 26, 24, 8, 34, 12, 35, 13, 32, 29, 44, 19, 45, 15, 18, 14, 57, 56, 16, 20, 58, 48, 25, 54, 73, 76, 72, 27, 75, 82, 62, 66, 84, 87, 71, 78, 95, 31, 74, 94, 97, 103, 22, 40, 39, 30, 86, 33, 41, 91, 46, 42, 117, 119, 122, 37
Offset: 0
Programs
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Mathematica
mex[s_] := Min[Complement[Range[0, Max[{s, -1}] + 1], Flatten[s]]]; f[s_] := Join[s, s + Table[i, {i, Length[s]}]]; T[n_, k_] := T[n, k] = mex[{f[Table[T[n - i, k], {i, n}]], f[Table[T[n, k - i], {i, k}]], f[Table[T[n - i, k - i], {i, Min[n, k]}]]}]; a[n_] := T[n, n]; Table[a[n], {n, 0, 69}] (* Jean-François Alcover, Aug 19 2019, from A018219 Mma code *)
Extensions
Edited and extended by Christian G. Bower, Oct 29 2002