Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II

Details Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II

2011-01-07

arxiv.org/abs/1101.1516v4

Mathematics

Combinatorics

57 pages, 8 figures

Scientific paper

We deliver here second new $\textit{H(x)}-binomials'$ recurrence formula, were $H(x)-binomials' $ array is appointed by $Ward-Horadam$ sequence of functions which in predominantly considered cases where chosen to be polynomials . Secondly, we supply a review of selected related combinatorial interpretations of generalized binomial coefficients. We then propose also a kind of transfer of interpretation of $p,q-binomial $ coefficients onto $q-binomial$ coefficients interpretations thus bringing us back to $Gy{\"{o}}rgy P\'olya $ and Donald Ervin Knuth relevant investigation decades ago.

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