$n$-Colour self-inverse compositions

Details $n$-Colour self-inverse compositions $n$-Colour self-inverse compositions

2006-08-31

arxiv.org/abs/math/0608776v1

Mathematics

Combinatorics

10 pages

Scientific paper

MacMahon's definition of self-inverse composition is extended to $n$-colour self-inverse composition. This introduces four new sequences which satisfy the same recurrence relation with different initial conditions like the famous Fibonacci and Lucas sequences. For these new sequences explicit formulas, recurrence relations, generating functions and a summation formula are obtained. Two new binomial identities with combinatorial meaning are also given.

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