On (Almost) Realizable Subsequences of Linearly Recurrent Sequences
Florian Luca
School of Mathematics
University of the Witwatersrand
1 Jan Smuts Avenue
Braamfontein 2050
Johannesburg
South Africa
and
Max Planck Institute for Software Systems
Saarland Information Campus E1 5
66123 Saarbrücken
Germany
and
Centro de Ciencias Matemáticas UNAM
Morelia
México
Thomas Ward
Department of Mathematical Sciences
Durham University
Durham DH1 3LE
England
Abstract:
We show that if (un)n≥1
is a simple linearly recurrent sequence of integers
whose minimal recurrence of order k involves only
positive coefficients that has positive initial terms, then
(Muns)n≥1
is the sequence of periodic point counts for some map for a suitable
positive integer M and s any sufficiently large multiple
of k!. This extends a result of Moss and Ward who proved the same
result for the Fibonacci sequence.
Full version: pdf,
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(Concerned with sequences
A000045
A000073
A000079
A000204
A054783.)
Received March 24 2023; revised version received May 4 2023.
Published in Journal of Integer Sequences,
May 5 2023.
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