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Workarounds :

sage: import sympy
sage: sympy.limit(*map (sympy.sympify, (UUan, n, oo)))._sage_()
1/4*(a^2 + 3*a + 4)/2^a
sage: mathematica.Limit(UUan, mathematica.Rule(n, oo))._sage_()
(a^2 + 3*a + 4)*2^(-a - 2)

Fricas and Giac have some unfelicities in this department...

Workarounds :

sage: import sympy
sage: sympy.limit(*map (sympy.sympify, (UUan, n, oo)))._sage_()
1/4*(a^2 + 3*a + 4)/2^a

Or, more simply :

sage: limit(UUan, n=oo, algorithm="sympy")
1/4*(a^2 + 3*a + 4)/2^a

Also :

sage: mathematica.Limit(UUan, mathematica.Rule(n, oo))._sage_()
(a^2 + 3*a + 4)*2^(-a - 2)

Fricas and Giac have some unfelicities infelicities in this department...