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Default Using SUM + INDEX in array formula

I'm having problems getting an array formula like this to work:
=SUM(INDEX(Data_Table,Row_Index_List,Col_Index_Lis t))

Basically, I have two columns of numbers that represent the row and column
indexes from a data table (ranges Row_Index_List and Col_Index_List). I want
to look up the numbers in the corresponding row/column of range Data_Table,
and return the sum of all returned values.

More detail: Row_Index_List and Col_Index_List are columns of (let's say)
100 cells, and Data_Table is a 7*5 range on the same sheet.

It looks like the combination of SUM(INDEX(..)) does not work in an array
formula. Can anyone suggest anything different. I have tried combinations of
SUMIF, OFFSET, INDIRECT, SUMPRODUCT, but none seem to work. SUMIF gets close,
but seems to return an array that is offset from the result I would expect.

Thanks,
Dave
 
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