Let a combination of buttons be a Sequence of disjoint nonempty Subsets of the Set
. If the number of possible combinations is denoted , then satisfies the Recurrence
Relation
(1) |
(2) |
(3) |
(4) |
(5) |
The quantity
(6) |
(7) |
References
Sloane, N. J. A. Sequence
A000670/M2952
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
Velleman, D. J. and Call, G. S. ``Permutations and Combination Locks.'' Math. Mag. 68, 243-253, 1995.