𝑛-Colour Self-Inverse Compositions

[摘要] 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.

[学科分类] 数学（综合）

[关键词] Compositions;𝑛-colour compositions;self-inverse compositions;sequences;recurrence formulas;generating functions;binomial identities.