Moessnerian theorems. How to prove them by simple graph theoretical inspection (Q750485)

The paper contains a very nice graph-theoretical proof and some generalizations of the following well-known theorem by Moessner: For natural k perform the following algorithm: STEP 1: Write down the sequence of integers. STEP t (2\(\leq t\leq k):\) leave out every \((k-2+t)\)-th term of the preceding sequence and write down the partial sums of the remaining sequence. Then, at step k, we end up with the sequence of k-th powers of naturals.