Wolfdieter Lang

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Sequences of generalized Stirling numbers of both kinds are introduced. These sequences of triangles (i.e. infinite-dimensional lower triangular matrices) of numbers will be denoted by S2(k; n, m) and S1(k; n, m) with k ∈ Z. The original Stirling number triangles of the second and first kind arise when k = 1. turns out to be Catalan's triangle. Generating(More)
Motivated by recent work of Trümper, we consider the general Collatz word (up-down pattern) and the sequences following this pattern. We derive recurrences for the first and last sequence entries from repeated application of the general solution of a binary linear inhomogeneous Diophantine equation. We solve these recurrences and also discuss the Collatz(More)
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