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MATHEMATICA
| M = {{0, 1, 0, 1, 1, 0, 0, 1}, {1, 0, 1, 0, 1, 1, 0, 0}, {0, 1, 0, 1, 0, 1, 1, 0}, {1, 0, 1, 0, 0, 0, 1, 1}, {1, 1, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0}, {1, 0, 0, 1, 0, 0, 0, 0}}
v[1] = Table[Fibonacci[n], {n, 1, 8}] v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
CoefficientList[Series[x (1+30x+49x^2-71x^3-116x^4)/((2x+1)(4x^2+2x-1) (2x^2-1)), {x, 0, 30}], x] (* From Harvey P. Dale, Jul 24 2011 *)
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