When Elvish Promenade resolves while Mana Echoes is on the field, the player receives colorless mana for each elf that enters the battlefield. Example:
The player has three elves and casts promenade, getting 3 more elves. The first elf from promenade (fourth on the board) gives 4 The second elf from promenade (fifth on the board) gives 5 The third elf from promenade (sixth on the board) gives 6
The formula for figuring out the amount of colorless mana a player receives is: (X(X+1))/2 - (Y(Y+1))/2 where X is the total number of elves after promenade resolves and Y is the number of elves before promenade resolves.