In this paper we investigate dark matter structure formation in the normal branch of the Dvali-Gabadadze-Porrati (nDGP) model using the PINOCCHIO algorithm. We first present 2nd order Lagrangian perturbation theory for the nDGP model, which shows that the 1st- and 2nd-order growth functions in nDGP are larger than those in ΛCDM. We then examine the dynamics of ellipsoidal collapse in nDGP, which is accelerated compared to ΛCDM due to enhanced gravitational interactions. Running the nDGP-PINOCCHIO code with a box size of 512 Mpc h -1 and 10243 particles, we analyze the statistical properties of the output halo catalogs, including the halo power spectrum and halo mass function. The calibrated PINOCCHIO halo power spectrum agrees with N-body simulations within 5% in the comoving wavenumber range k<0.3 (h Mpc-1) at redshift z=0. The agreement is extended to smaller scales for higher redshifts. For the cumulative halo mass function, the agreement between N-body and PINOCCHIO is also within the simulation scatter.
