Name
Abstract | ||
|---|---|---|
The generalized Hosoya triangle is an arrangement of numbers where each entry is a product of two generalized Fibonacci numbers. We define a discrete convolution C based on the entries of the genealized Hosoya triangle. We use C and generating functions to prove that the sum of every k-th entry in the n-th row or diagonal of generalized Hosoya triangle, beginning on the left with the first entry, is a linear combination of rational functions on Fibonacci numbers and Lucas numbers. A simple formula is given for a particular case of this convolution. We also show that C summarizes several sequences in the OEIS. As an application, we use our convolution to enumerate many statistics in combinatorics. |
Year | Venue | Keywords |
|---|---|---|
2015 | JOURNAL OF INTEGER SEQUENCES | Hosoya triangle,generalized Fibonacci number,convolution,non-decreasing Dyck path,Fibonacci binary word |
DocType | Volume | Issue |
Journal | 18 | 1 |
ISSN | Citations | PageRank |
1530-7638 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Éva Czabarka | 1 | 0 | 0.34 |
| Rigoberto Flórez | 2 | 0 | 0.68 |
| Leandro Junes | 3 | 0 | 0.68 |