论文标题
Pascal-Dellanoy三角形的不对称扩展
Asymmetric extension of Pascal-Dellanoy triangles
论文作者
论文摘要
我们给出了称为准S-Pascal三角形的Pascal三角形的概括，其中越过对角线射线的元素的总和产生了S-Bonacci序列。为此，考虑平面中的晶格路径，其步骤集为{l =（1，0），l1 =（1，1），l2 =（2，1），。 。 。 ，ls =（s，1）};给出了明确的公式。从而将准S-Pascal三角形的元素与双向系数联系起来。我们建立了在准S-Pascal三角形的任何有限射线上的元素之和的复发关系。产生了引用总和的生成函数。我们还提供了同等的身份，并建立了准S-Pascal三角形系数的Q-Analeogue。
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 finite ray of the quasi s-Pascal triangle. The generating function of the cited sums is produced. We also give identities among which one equivalent to the de Moivre sum and establish a q-analogue of the coefficient of the quasi s-Pascal triangle.
