# T-MODELS APPLICATION FOR INTEGER SEQUENCES INTERPOLATION

**Author(s):**
Bondarenko L.N.

**Rubric:**
Methodological research

**DOI: **
10.21777/2500-2112-2021-3-97-105

**Release:**
2021-3 (36)

**Pages:**
97-105

**Keywords:**
sequence interpolation, T-models, Lehmer codes, generalized Catalan numbers, generalized Bell numbers, qanalogue

**Annotation:**
The article proposes a new technique for interpolating integer sequences. It is demonstrated on classes interpolating
sequences between Catalan numbers and factorials and between Bell numbers and factorials as well. This
technique is based on T-models and Lehmer permutations codes. T-models are specified recursively by sequences
of special type numerical tables. It allows us to obtain algorithms for solving a number of emerging problems.
Integer sequences correspond to T-models whereas sets of numbers (codes) of their elements are also constructed
for the latter. Using this technique the article introduces the classes of generalized Catalan and Bell numbers,
as well as their q-analogues. Their extension leads to the sequence interpolation problem solution. We also find
the permutation classes corresponding to sequences and given by sets of Lehmer codes. This approach greatly
simplifies the construction of permutation classes that were previously obtained in computer science articles by
means of removing the permutations with given patterns.

**Bibliography:**
Bondarenko L.N. T-MODELS APPLICATION FOR INTEGER SEQUENCES INTERPOLATION // Education Resources and Technologies. – 2021. – № 3 (36). – С. 97-105. doi: 10.21777/2500-2112-2021-3-97-105