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Let the coefficient of x^(r) in the expa...

Let the coefficient of `x^(r)` in the expansion of `(x+3)^(n-1)+(x+3)^(n-2)(x+2)+(x+3)^(n-3)(x+2)^(2)+........+(x+2)^(n-1)` be `alpha_(r)` .If `sum_(r=0)^(n)alpha_(r)=beta^(n)-gamma^(n),beta,gamma in NN` ,then the value of `beta^(2)+gamma^(2)` equals:

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