  The Gromov-Witten invariants of \mathbb{C}^3 with branes is encoded in the
topological vertex which has a very complicated combinatorial expression. A
simple formula for the topological vertex was proposed by Aganagic et al in the
fermionic picture. We will propose a similar formula for the framed topological
vertex and prove it in the case when there are one or two branes.
