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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
OEIS
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