Given the first terms of a sequence of numbers, we can compute potential recurrence equations the sequence satisfies by choosing a suitable template recurrence with undetermined coefficients, matching it against the given sequence sample, obtaining a system of constraints on the undetermined coefficients and solving this system. Of particular interest are linear recurrence equations p_0(n) f(n) + p_1(n) f(n+1) + ... + p_r(n) f(n+r) of order r where the p_i(n) are polynomials in n of degree d. Order r and degree d have to be somehow chosen a priori. But how? There are two strategies. One consists of making r as small as possible and d as big as necessary, and the other consists of taking d and r approximately balanced. In large scale examples, both strategies have appealing advantages as well as prohibitive disadvantages. We will show how the two strategies can be combined such that the advantages take effect and the disadvantages are avoided. We will comment on some recent applications of this method in combinatorics, particle physics and partition theory. Finally, we will speculate about possible multivariate generalizations.
Forschungs-