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Formula Formulation (Posted on 20140303) 

A function f(N) is defined as:
f(1)=sod(1^{2}), f(2) = sod(12^{2})
f(3) = sod(121^{2}), f(4) = sod(1212^{2}), .... and, so on
Derive the general formula for f(N) in terms of N.
*** sod(x) denotes the sum of the digits of base ten expansion of x.
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