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Integer Sequences Related to Compositions without 2's
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Phyllis Chinn

Department of Mathematics

Humboldt State University

Arcata, CA 95521

USA

Silvia Heubach

Department of Mathematics

California State University, Los Angeles

Los Angeles, CA 90032

USA

**Abstract:**
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, 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.

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(Concerned with sequences
A005251
A008778
A002411
A008779
A005314
A000931
A078027
.)

Received January 24, 2002;
revised version received July 2, 2003.
Published in *Journal of Integer Sequences* July 8, 2003.

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