A naive implementation of doing some counting after data logic for a list of dates and a given source data frame.

SHSViking Date Comparisons

# Generate your list of dates
mydays <- seq.Date( as.Date('2015-01-01'), as.Date('2015-03-09'), by="day")

# Write function to sum the number of open dates that occur in sourceData at least 31 days prior to given date.
numOpenDates <- function( givenDate ){
  retValue <- sum( (givenDate - sourceDate$openDate) > 30 )
  retValue
}

# Apply function to each date in your list of dates(mydays)
answer <- lapply(X=mydays, FUN=numOpenDates)