Journal of Integer Sequences, Vol. 6 (2003), Article 03.2.3

Integer Sequences Related to Compositions without 2's

Phyllis Chinn
Department of Mathematics
Humboldt State University
Arcata, CA 95521

Silvia Heubach
Department of Mathematics
California State University, Los Angeles
Los Angeles, CA 90032

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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