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Integer sequences related to compositions without \(2\)’s. (English) Zbl 1036.05004
Summary: A composition of a positive integer \(n\) consists of an ordered sequence of positive integers whose sum is \(n\). We investigate compositions in which the summand 2 is not allowed, and count the total number of such compositions and the number of occurrences of the summand \(i\) in all such compositions. Furthermore, we explore patterns in the values for \(C_{j}(n,\widehat{2})\), the number of compositions of \(n\) without 2’s having \(j\) summands, and show connections to several known sequences, for example the \(n\)-dimensional partitions of 4 and 5.

MSC:
05A17 Combinatorial aspects of partitions of integers
11B37 Recurrences
Software:
OEIS
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