is the number of possible configurations of a quiescent
board. It's the evaluation of the function
: the function itself would have 20
as a variable
\ / \ n
\ | 10 |
1 + / | 2 - 2 |
/ \ /
n = 1
The explanation for this: each possible Tetris row has one of 2^10 (1024) possible configurations, as each space may be in the state of a block "present" or "not present". There is one possible configuration which does not have any rows, the completely empty board, which accounts for the 1 in the equation.
The number of possible boards with exactly one non-empty row is 1022 (2^10 - 2), as no completely empty rows are allowed below any non-empty rows, and any full rows will be cleared. As for the number of boards with exactly two non-empty rows, it will be (2^10 - 2)^2, and so on from 1 through 20. Using sigma notation, the number is the summation which evaluates to the aforementioned huge number.