Geodesic
A Note on a Theorem of Moser and Whitney
Canadian mathematical bulletin, Tome 5 (1962) no. 2, pp. 191-194

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In a recent paper [1], L. Moser and E.L. Whitney have proved the following.Theorem: The number of compositions of n into parts=1, 2, 4 or 5 (mod 6) and involving an even number of parts=4 or 5 (mod 6) exceeds by n the number of compositions of n into parts=1, 2, 4 or 5 (mod 6) and involving an odd number of parts=4 or 5 (mod 6).Their method of proof utilizes the notion of weighted compositions and the method of generating series. They remark that they have not been able to find a direct combinatorial proof. The purpose of this note is to give a direct proof of a more general result. 
Narayana, T. V.; Pettigrew, H. M. A Note on a Theorem of Moser and Whitney. Canadian mathematical bulletin, Tome 5 (1962) no. 2, pp. 191-194. doi: 10.4153/CMB-1962-020-0
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     title = {A {Note} on a {Theorem} of {Moser} and {Whitney}},
     journal = {Canadian mathematical bulletin},
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     year = {1962},
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     number = {2},
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