Wiktionary
reckon upon
vb. 1 To count upon or depend upon. 2 To plan upon; to expect.
Usage examples of "reckon upon".
For I reckon upon it as a Certainty, that when you have acquitted your last Promise, you embark in another.
On the other hand, to reckon upon the animosities and to segregate hostile factions seemed to Aillas the worst of all solutions, since it would give the feuds official recognition.
Those pounds, however, would be needed for the rent, so I could hardly reckon upon them at all, as far as my immediate wants went.