The N2R4
The N2R4 is a FIDE Rook whose move is limited to a distance of 4 squares (from a1 to e1, for example), PLUS a Knight-rider whose move is limited to two steps.For example, from f1 it can use its Rookish powers to go to e1, and then if e1 is empty to continue in the same move to d1, c1, and b1 (but not to a1 because that would be too far); or it can go Rookishly to e2, e3, e4, e5 (but not e6 or further); or Rookishly to g1 and h1. In addition, it can use its Knightrider powers to move from f1 to e3, and then if e3 is empty it can continue in the same move to d5 (but then can go no further in this direction); or g3, h5; or d2, b3.
The value of this piece is supposed to be the same as a Queen.