SymPy Gamma

SymPy:

rsolve (y(n+2)-y(n+1)-y(n),y(n))

$\mathrm{Solve~the~recurrence~}- y{\left (n \right )} - y{\left (n + 1 \right )} + y{\left (n + 2 \right )} = 0$

Result:

$C_{0} \left(\frac{1}{2} + \frac{\sqrt{5}}{2}\right)^{n} + C_{1} \left(- \frac{\sqrt{5}}{2} + \frac{1}{2}\right)^{n}$

2**(-n)*(C0*(1 + sqrt(5))**n + C1*(-sqrt(5) + 1)**n)

$2^{- n} \left(C_{0} \left(1 + \sqrt{5}\right)^{n} + C_{1} \left(- \sqrt{5} + 1\right)^{n}\right)$

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