Numpy has a direct solution, so get your data into an array either using tabletonumpyarray or featureclasstonumpyarray or whatever
>>> a
array([[ 0, 0, 2013, 0, 2015],
[2011, 2112, 2013, 0, 2015],
[2011, 0, 0, 2014, 2015],
[2011, 0, 2013, 2014, 0]])
>>> np.sum(np.where(a !=0, 1,0), axis=1)
array([2, 4, 3, 3])