Research Article
Integer Sequences in the HP Model of Dill
@INPROCEEDINGS{10.1007/978-3-031-17292-2_13, author={Slav Angelov and Latchezar Tomov}, title={Integer Sequences in the HP Model of Dill}, proceedings={Computer Science and Education in Computer Science. 18th EAI International Conference, CSECS 2022, On-Site and Virtual Event, June 24-27, 2022, Proceedings}, proceedings_a={CSECS}, year={2022}, month={11}, keywords={Dill’s HP model Square lattice Quarter square Spiral Positive integer sequence}, doi={10.1007/978-3-031-17292-2_13} }- Slav Angelov
Latchezar Tomov
Year: 2022
Integer Sequences in the HP Model of Dill
CSECS
Springer
DOI: 10.1007/978-3-031-17292-2_13
Abstract
We examine a sequence that we derive from Dill’s hydrophobic-polar protein folding model in a two-dimensional square lattice. This sequence already exists asA248333in the OEIS, but the information is scarce. We construct two more sequences not previously listed in the OEIS,A342711andA342712. Thanks to the perspective given us by Dill’s model, we find relationships between sequences248333,A240025,A000267,A342711,A342712,000027, andA000217. We use the newly found relationships to obtain an explicit formula for thenth member ofA248333and a formula for thenth member of its partial sums,A342712. Moreover, we find an explicit formula for thenth member ofA342711and present an alternative proof for thenth member ofA000267.
Copyright © 2022–2025 ICST
