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n-Colour self-inverse compositions

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Abstract

MacMahon’s definition of self-inverse composition is extended ton-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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Authors and Affiliations

  1. Centre for Advanced Studies in Mathematics, Panjab University, 160 014, Chandigarh, India

    Geetika Narang & A. K. Agarwal

Authors
  1. Geetika Narang
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  2. A. K. Agarwal
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Correspondence to Geetika Narang.

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Narang, G., Agarwal, A.K. n-Colour self-inverse compositions. Proc. Indian Acad. Sci. (Math. Sci.) 116, 257–266 (2006). https://doi.org/10.1007/BF02829743

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  • DOI: https://doi.org/10.1007/BF02829743

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