  Recent observations have demonstrated a significant growth in the integrated
stellar mass of the red sequence since z=1, dominated by a steadily increasing
number of galaxies with stellar masses M* < 10^11 M_sun. In this paper, we use
the COMBO-17 photometric redshift survey in conjunction with deep Spitzer 24
micron data to explore the relationship between star formation and the growth
of stellar mass. We calculate `star formation rate functions' in four different
redshift slices, splitting also into contributions from the red sequence and
blue cloud for the first time. We find that the growth of stellar mass since
z=1 is consistent with the integrated star formation rate. Yet, most of the
stars formed are in blue cloud galaxies. If the stellar mass already in, and
formed in, z<1 blue cloud galaxies were to stay in the blue cloud the total
stellar mass in blue galaxies would be dramatically overproduced. We explore
the expected evolution of stellar mass functions, finding that in this picture
the number of massive M* > 3x10^10 M_sun blue galaxies would also be
overproduced; i.e., most of the new stars formed in blue cloud galaxies are in
the massive galaxies. We explore a simple truncation scenario in which these
`extra' blue galaxies have their star formation suppressed by an unspecified
mechanism or mechanisms; simple cessation of star formation in these extra blue
galaxies is approximately sufficient to build up the red sequence at M*<10^11
M_sun.
