The number of non-negative integral solutions of x1 + x2 + x3 + 4x4 = 20 is

Number of non-negative integral solutions of the given equation= coefficient of x20 in(1−x)−1(1−x)−1(1−x)−11−x4−1.= coefficient of x20 in (1−x)−31−x4−1= coefficient of x20 in 1+3C1x+4C2x2+5C3x3+6C4x4+…+10C8x8…+14C12x12+…+18C16x16+…+22C20x20+…×1+x4+x8+x12+x16+x20+…=1+6C4+10C8+14C12+18C16+22C20=1+6C2+10C2+14C2+18C2+22C2=1+6.51.2+10.91.2+14.131.2+18.171.2+22.211.2=1+15+45+91+153+231=536.