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