Just add another constructor overload:
A(int ia, int ib)
: a(ia), b(ib), c(ia + ib) {}
A(int ia, int ib, int ic)
: a(ia), b(ib), c(ic) {}
For more complex initialisation, you can avoid repetition using a C++11 delegating constructor:
A(int ia, int ib)
: A(ia, ib, ia + ib) {}
A(int ia, int ib, int ic)
: a(ia), b(ib), c(ic) {}