| Popis: |
First we report our discovery by computer search of (4, n)-sequences with n=16, 18, 19 and 20 which are perfect according to an extended definition of the generalized Langford problem. Next we give the problem further consideration by introducing the generating function of the sequence with eimx as the indicator function. As a result we obtain fourteen properties concerning the Langford (s, n)-sequence particularly with s=4. Above all we note the properties of the sum and the number of φ(k), a function that assigns the positions in the sequence for a set of k. |
