Abstract
In the present paper, we consider a variation of the hyperbolic Pascal pyramid where the three leg-sequences (the constant 1 sequence) are replaced by the sequences \(\lbrace \alpha _n\rbrace _{n\ge 0}\), \(\lbrace \beta _n\rbrace _{n\ge 0}\) and \(\lbrace \gamma _n\rbrace _{n\ge 0}\) with \(\alpha _0=\beta _0=\gamma _0=\Omega \), and we describe the values of elements. Then we give the recurrence relations associated to the sums of the values on levels in the generalized hyperbolic Pascal’s pyramids. The order of these recurrences is six.
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Acknowledgements
For H. Belbachir and F. Rami the paper is partially supported by the DGRSDT grant No. C0656701. For L. Szalay the research and this work was supported by Hungarian National Foundation for Scientific Research Grant No. 128088, and No. 130909, and by the Slovak Scientific Grant Agency VEGA 1/0776/21.
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Communicated by Shariefunddin Pirzada.
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Belbachir, H., Rami, F., Németh, L. et al. A generalization of the hyperbolic Pascal pyramid. Indian J Pure Appl Math (2023). https://doi.org/10.1007/s13226-023-00481-4
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DOI: https://doi.org/10.1007/s13226-023-00481-4