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MATHEMATICA
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M = {{0, 0, 0, 1}, {1, 5, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 5}};
v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M.v[n - 1]; terms = 20; a = Table[v[n][[1]], {n, 1, terms}]
LinearRecurrence[{10, -25, 0, 1}, {0, 2, 11, 56}, 30] (* Harvey P. Dale, Nov 29 2018 *)
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