  Assuming sufficiently many terms of a n-dimensional table defined over a
field are given, we aim at guessing the linear recurrence relations with either
constant or polynomial coefficients they satisfy. In many applications, the
table terms come along with a structure: for instance, they may be zero outside
of a cone, they may be built from a Gr{\"o}bner basis of an ideal invariant
under the action of a finite group. Thus, we show how to take advantage of this
structure to both reduce the number of table queries and the number of
operations in the base field to recover the ideal of relations of the table. In
applications like in combinatorics, where all these zero terms make us guess
many fake relations, this allows us to drastically reduce these wrong guesses.
These algorithms have been implemented and, experimentally, they let us handle
examples that we could not manage otherwise. Furthermore, we show which kind of
cone and lattice structures are preserved by skew polynomial multiplication.
This allows us to speed up the guessing of linear recurrence relations with
polynomial coefficients by computing sparse Gr{\"o}bner bases or Gr{\"o}bner
bases of an ideal invariant under the action of a finite group in a ring of
skew polynomials.
