Advances and Applications in Discrete Mathematics
Volume 28, Issue 2, Pages 357 - 368
(November 2021) http://dx.doi.org/10.17654/DM028020357 |
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NUMBER OF SUBSETS OF THE SET INCLUDING NO TWO CONSECUTIVE ODD INTEGERS
Kemal Uslu and Barış Arslan
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Abstract: Fibonacci sequence and similar integer sequences are used in many fields from engineering to arts besides basic sciences and mathematics. For every let be the number of subsets of S of the set including no two consecutive odd integers. We give the generating function and the closed formula of the sequence obtaining fourth order linear homogeneous recurrence relation with constant coefficients of the integer sequence. The sequence is associated with the Fibonacci sequence and the combinatorial representation of is obtained.
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Keywords and phrases: Fibonacci numbers, consecutive odd integers, generating functions, combinatorial representation.
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