A connection between a special kind of walks in the XY -plane studied by J.H. van Lint and R.M. Wilson  and n-colour compositions introduced recently by A.K. Agarwal  is shown. This leads to several new combinatorial properties of the walks and also gives a new binomial identity with its combinatorial interpretation.
Keywords and Phrases
Walks, Fibonacci numbers, n-colour compositions, self-conjugate partitions, odd-even partitions, generating function, recurrence formula, binomial identity, combinatorial properties.
A.M.S. subject classiﬁcation
05A15, 05A17, 11P81.