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Prove Identities for Sequences
Prove identities for holonomic sequences.
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PellP = DifferenceRoot[

   Function[{y, n}, {-y[n] - 2 y[1 + n] + y[2 + n] == 0, y[0] == 0, 

     y[1] == 1}]];
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DifferenceRootReduce[

 PellP[n] == (-(1 - Sqrt[2])^n + (1 + Sqrt[2])^n)/(2 Sqrt[2]), n]
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DifferenceRootReduce[PellP[n + 1] PellP[n - 1] - PellP[n]^2 == (-1)^n,

  n]
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DifferenceRootReduce[\!\(

\*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(4\ n + 1\)]\(PellP[

    i]\)\) == (PellP[2 n + 1] + PellP[2 n])^2, n]
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