how many more squares can a given (fairy) chess piece reach in N+1 moves over N moves? first differences of range function.
for wazir, ferz, dabbaba, or alfil, on an otherwise empty infinite board, the sequence is 4, 8, 12,... (multiples of 4).
king: 8 16 24 ... (multiples of 8).
to do: knight.
to do: compute for a finite board. average over possible initial positions.
these sequences allow comparing different fairy chess pieces. also more dimensions, other grids and graphs.
probably only useful for non-ranged pieces.
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