I have a Google Analytics account with a well-functioning funnel made up of 4 goals.  I can query the API and get the data out, but it does not match the funnel report in Analytics.  Without getting into specific values, I can give you an example with faked data.
Here's how the funnel might look:
Shopping Cart
100 > 100 > 20
       80 (80%)
Address Page
5   >  85 > 25
       60 (71%)
Payment Page
2   >  62 > 10
       52 (84%)
Checkout
1   >  53
      (49.07% funnel conversion rate)
Okay, so you would expect the API to output data something like this:
goal1Starts goal1Completions goal1Abandons
100         80               20
goal2Starts goal2Completions goal2Abandons
85          60               25
goal3Starts goal3Completions goal3Abandons
62          52               10
goal4Starts goal4Completions goal4Abandons
53          53               0
Instead, it's different.  Firstly, the abandons are associated with the following goal (so goal1 always has 0 abandons and goal4 always has 0 abandons.  Okay, I can work with that.  What's confusing is that the numbers are always a little different.  The goal1Completions always match the report, as do the goal4Completions, but everything else is off by a small amount.  Sometimes it's only 2 visits, other times it's off by 50.
For the report above here's the kind of results I would tend to get:
goal1Starts goal1Completions goal1Abandons
100         100              0
goal2Starts goal2Completions goal2Abandons
105         84               21
goal3Starts goal3Completions goal3Abandons
90          65               25
goal4Starts goal4Completions goal4Abandons
58          53               5
Here's what I know:
Goal(n)Completions + Goal(n)Abandons = Goal(n)Starts
Goal(n)Starts = Goal(n-1)Completions
Goal(n)Starts - Goal(n-1)Completions != reported number entering at that level
That third one is particularly disappointing.  So, here's my question:
What data do I need to pull from the API in order to recreate the counts in the Funnel report in Google Analytics?  I don't need the pages exited to entering from - just the counts at every level.