How many equilateral triangles with sides of 4 can fit into a larger triangle with sides of 2012

The base measures 2012 if you divide that by four you get 503 trianles on the bottom and on the sides and each one gets one smaller until you get to one so 503+502+501, ... or 252+251 (504) so the answer is 126,756 triangles in total because 1+503=504 2+502=504 ... when you get to 252 you just add that to itself so that is the odd one out