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

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.

Geetika Narang¹ A K Agarwal¹

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

Published

August 2006

Manuscript received

18 November 2005

Manuscript revised

12 April 2006