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    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/116/03/0257-0266

    • Keywords

       

      Compositions; n-colour compositions; self-inverse compositions; sequences; recurrence formulas; generating functions; binomial identities

    • 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.

    • Author Affiliations

       

      Geetika Narang1 A K Agarwal1

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

    • Dates

       
      Published
      August 2006
      Manuscript received
      18 November 2005
      Manuscript revised
      12 April 2006

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