The problem whether each element of a sequence satisfying a fourth order linear recurrence with integer coefficients is nonnegative, referred to as the Positivity Problem for fourth order linear recurrence sequence, is shown to be decidable.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-1-11, author = {Pinthira Tangsupphathawat and Narong Punnim and Vichian Laohakosol}, title = {The positivity problem for fourth order linear recurrence sequences is decidable}, journal = {Colloquium Mathematicae}, volume = {126}, year = {2012}, pages = {133-142}, zbl = {1284.11023}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-1-11} }
Pinthira Tangsupphathawat; Narong Punnim; Vichian Laohakosol. The positivity problem for fourth order linear recurrence sequences is decidable. Colloquium Mathematicae, Tome 126 (2012) pp. 133-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-1-11/