### Abstract

We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a basis of se- quences that can be obtained as the INVERT transform of the coefficients of the given recurrence relation. For such a basis sequence with generating function Y (t), and for any positive integer r, we give a formula for the convolved sequence generated by Y (t)^{r} and prove that it satisfies an elegant recurrence relation.

Original language | English (US) |
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Journal | Journal of Integer Sequences |

Volume | 18 |

Issue number | 1 |

State | Published - 2014 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics

### Cite this

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*Journal of Integer Sequences*, vol. 18, no. 1.

**Linear recurrence sequences and their convolutions via bell polynomials.** / Birmajer, Daniel; Gil, Juan Bautista; Weiner, Michael David.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Linear recurrence sequences and their convolutions via bell polynomials

AU - Birmajer, Daniel

AU - Gil, Juan Bautista

AU - Weiner, Michael David

PY - 2014

Y1 - 2014

N2 - We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a basis of se- quences that can be obtained as the INVERT transform of the coefficients of the given recurrence relation. For such a basis sequence with generating function Y (t), and for any positive integer r, we give a formula for the convolved sequence generated by Y (t)r and prove that it satisfies an elegant recurrence relation.

AB - We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a basis of se- quences that can be obtained as the INVERT transform of the coefficients of the given recurrence relation. For such a basis sequence with generating function Y (t), and for any positive integer r, we give a formula for the convolved sequence generated by Y (t)r and prove that it satisfies an elegant recurrence relation.

UR - http://www.scopus.com/inward/record.url?scp=84917690777&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84917690777&partnerID=8YFLogxK

M3 - Article

VL - 18

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

SN - 1530-7638

IS - 1

ER -