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a guest Mar 25th, 2019 61 Never
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  1. AbsoluteTiming[
  2.  g[n_] := n (3 n - 1)/2;
  3.  y[k_] := 1/6 (1 + 1/2 (-(7 - 4 Sqrt[3])^(1 + 2 k)
  4.         - Sqrt[3] (7 - 4 Sqrt[3])^(1 + 2 k)
  5.         - (7 + 4 Sqrt[3])^(1 + 2 k)
  6.         + Sqrt[3] (7 + 4 Sqrt[3])^(1 + 2 k)));
  7.  ans = Simplify@g@y[2]]
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