%N a(n) is the maximum number of moves available to one side from a legal chess position with n pieces with promoted pieces allowed.
%C For this sequence, unlike A275360, extra pieces from Pawn promotion are allowed in the original positions. For move counts, both of these sequences allow four promotion moves (to Knight, Bishop, Rook, or Queen) per Pawn per promotion square.
%C Clearly a(n) >= A275360(n) for all 2 <= n <= 32. Additional terms, positions, and proof games showing the legality of the positions -- especially for the larger n -- are desired for both of these sequences. - _Rick L. Shepherd_, Dec 31 2017
%e White has 8 + 27 + 25 + 25 + 23 = 108 possible moves in the legal position with White King on b5, White Queens on c7, d4, e6, and f3, and Black King on g5. Because there are 6 total pieces on the board and no other legal position with 6 pieces has more than 108 moves available for one side, a(6) = 108.
%Y Cf. A275360.
%A _Rick L. Shepherd_, Jan 15 2017