# Asymmetric extension of Pascal-Dellanoy triangles

@article{Amrouche2020AsymmetricEO, title={Asymmetric extension of Pascal-Dellanoy triangles}, author={Said Amrouche and Hac{\`e}ne Belbachir}, journal={arXiv: Combinatorics}, year={2020} }

We give a generalization of the Pascal triangle called the quasi s-Pascal triangle where the sum of the elements crossing the diagonal rays produce the s-bonacci sequence. For this, consider a lattice path in the plane whose step set is {L = (1, 0), L1 = (1, 1), L2 = (2, 1), . . . , Ls = (s, 1)}; an explicit formula is given. Thereby linking the elements of the quasi s-Pascal triangle with the bisnomial coefficients. We establish the recurrence relation for the sum of elements lying over any… CONTINUE READING

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