### recurrence-rsolve-check

I am was testing some ideas and don't understand where this went wrong.

```
from sympy import Function, rsolve
from sympy.abc import n
y = Function('y');z=Function('z')
f = y(n)-y(n-1)-(-1)^n*binomial(x,n);g=z(n)-z(n-1)-binomial(x,n)
```

f is the sume of alternating binomial coefficients which is known.

g is just the summation of binomial coefficients (purportedly nonexistent)

```
frec = rsolve(f,y(n),{y(0):1});grec = rsolve(g,z(n),{z(0):1})
frec
```

--

```
zrec
```

Now this is correct, the alternating sum of binomials

```
fdiff = frec-(frec.subs({n : n-1}))
simplify(fdiff)
```

Whereas this is not correct?

```
gdiff = grec-(grec.subs({n : n-1}))
simplify(gdiff)
```

Am I missing something in rsolve usage?