How many integer solutions are there to the inequality y1 y

How many integer solutions are there to the inequality y_1 + y_2 + y_3 + y_4 0, 0

If we add Y2,y3,y4 solutions 10+17+19 we have 46 max value of integer which are less than 184 if y1 is 184-46=138

Y1 should be less than 138 if all are maximum

If all are minimum y1 is less than 183

So we have a pair starts from (182,1,0,0),(181,2,0,0),(180,3,0,0)....(173,10,0,0)

Like that for every value we have total 10+18+19=47 pairs which satisfy the inequality