Journal of Integer Sequences, Vol. 27 (2024), Article 24.7.8

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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