A formula for the Permanent of a Matrix
It turns out that the number of disks moved after the th step in the Towers of Hanoi is the same as the element which needs to be added or deleted in the th Addend of the Ryser formula (Gardner 1988, Vardi 1991, p. 111).
See also Determinant, Gray Code, Permanent, Towers of Hanoi
References
Gardner, M. ``The Icosian Game and the Tower of Hanoi.'' Ch. 6 in
The Scientific American Book of Mathematical Puzzles & Diversions. New York: Simon and Schuster, 1959.
Knuth, D. E. The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 3rd ed.
Reading, MA: Addison-Wesley, p. 515, 1998.
Nijenhuis, A. and Wilf, H. Chs. 7-8 in Combinatorial Algorithms. New York: Academic Press, 1975.
Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, p. 111, 1991.