ax₁+bx₂+cx₃= n

where x₁ x₂ x₃ are integers

a_i <= x_i <=b_i  (i= 1 , 2 , 3)

coeff of xⁿ  in  [ (x^a)^{a_{1   +}} (x^a )^a₁+1.....upto x power a power b₁  )] [ .....] [ ....]

in the second bracket instead of a put b ...that is coeff of x₂ and instead of a1 ...put a₂ to b₂    

similarly third bracket u put c _instead of a and change substcripts to 3 from 2

 

according to given sum

a=2       0<=x₁<= 10

b=1       0<=x₂<=20

c=1       0<=x₃<=20

so second and third bracket become [ 1+ x + x²+ ....x²⁰] each

first bracket

[1+x²+x⁴+ ...x²⁰ ] 

so question nothing but finding coeff of x power 20

in [1+x²+x⁴+ ...x²⁰ ] [ 1+ x + x²+ ....x²⁰][ 1+ x + x²+ ....x²⁰]

this is the method