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Published in:
2022 | OriginalPaper | Chapter
Integer Sequences in the HP Model of Dill
Authors : Slav Angelov, Latchezar Tomov
Published in: Computer Science and Education in Computer Science
Publisher: Springer Nature Switzerland
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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 as A248333 in the OEIS, but the information is scarce. We construct two more sequences not previously listed in the OEIS, A342711 and A342712. Thanks to the perspective given us by Dill’s model, we find relationships between sequences 248333, A240025, A000267, A342711, A342712, 000027, and A000217. We use the newly found relationships to obtain an explicit formula for the nth member of A248333 and a formula for the nth member of its partial sums, A342712. Moreover, we find an explicit formula for the nth member of A342711 and present an alternative proof for the nth member of A000267.