As far as we know, usual computer algebra packages can not compute denumerants for almost medium (about a hundred digits) or almost medium-large (about a thousand digits) input data in a reasonably time cost on an ordinary computer. Implemented algorithms can manage numerical n-semigroups for small input data. Basically, the denumerant of a non-negative element s ¿ N is the number of non-negative integer solutions of certain linear non-negative Diophantine equation which constant term is equal to s. Here we are interested in denumerants of numerical 3-semigroups which have almost medium input data. A new algorithm for computing denumerants is given for this task. It can manage almost medium input data in the worst case and medium-large or even large input data in some cases.

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Quaestiones mathematicae on 2018, available online at: http://www.tandfonline.com/10.2989/16073606.2017.1419998.