Yup. Both of my kids.
Sounds like it's an eat, play, sleep cycle. Is he/she babywise baby?
The eat, play, sleep cycle worked well for us because 1) DS was a huge reflux baby and had to be totally upright for 30 minutes after eating and 2) it helped to not make food/sleep associations which in turned helped with him sleeping own his own.
Even now I usually have my DCK's read for about 20 minutes after lunch before laying down. Unless they are being unruly, in which case lunch then nap it is