Allowing or Prohibiting Two Consecutive Colors in n-Color Compositions
Brian Hopkins
Department of Mathematics and Statistics
Saint Peter's University
Jersey City, NJ 07306
USA
Hua Wang
Department of Mathematical Sciences
Georgia Southern University
Statesboro, GA 30460
USA
Abstract:
Agarwal introduced n-color compositions in 2000 and subsequent
research has considered both restricting which parts are allowed and,
more recently, which colors are allowed. Here we consider allowing
or prohibiting two consecutive colors, focusing on several cases that
connect with other types of compositions. We also prove several identities
for certain tribonacci numbers. Most proofs are combinatorial, several
using the notion of spotted tilings introduced by the first named author
in 2012.
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(Concerned with sequences
A000045
A001333
A001590
A005314
A034943
A070550.)
Received June 26 2024; revised version received October 9 2024.
Published in Journal of Integer Sequences,
October 16 2024.
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