Geodesic
Integer sequences related to compositions without \(2\)'s
Journal of integer sequences, Tome 6 (2003) no. 2
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.
Classification : 05A99
Keywords: compositions, palindromes, n-dimensional partitions, pentagonal pyramidal numbers, square numbers, triangle numbers, tilings 
@article{JIS_2003__6_2_a2,
     author = {Chinn,  Phyllis and Heubach,  Silvia},
     title = {Integer sequences related to compositions without \(2\)'s},
     journal = {Journal of integer sequences},
     year = {2003},
     volume = {6},
     number = {2},
     zbl = {1036.05004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_2_a2/}
}
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Chinn,  Phyllis; Heubach,  Silvia. Integer sequences related to compositions without \(2\)'s. Journal of integer sequences, Tome 6 (2003) no. 2. http://geodesic.mathdoc.fr/item/JIS_2003__6_2_a2/