The number of functions f:{1,2,3,4}→{a∈Z:|a|≤8} satisfying f(n)+1nf(n+1)=1,∀n∈{1,2,3} is #jee

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consider a function f: N→R, satisfying f(1) +2f(2) + 3f(3)+...........+ xf(x) = x(x+1)f(x); consider a function f: N→R, satisfying f(1) +2f(2) + 3f(3)+...........+ xf(x) = x(x+1)f(x);