Spiked Math: Telephone Numbers

Greg Bernhardt

More...

Jimmy Snyder

The definition for n_0 can be taken as there is only one way to connect 0 subscribers, i.e. no connections. The same for n_1, there is only one way to connect 1 subscriber, no connections. For n_2, there are two ways, i.e. no connection, or connect the 2 subscribers.

For n_3, there are four ways. 1: no connections, 2: (12) 3: (23) 4: (13)

For the rest, you can simply list the idempotent elements of the permutation group. For instance n_4:
(1) (12) (13) (14) (23) (24) (34) (12)(34) (13)(24) (14)(23)
Note that the first of these represents no connections, the next six represent a single connection (with the other pair unconnected), the last three represent two connected pairs.