A function f(N) is defined as:
f(1)=sod(1²), f(2) = sod(12²)
f(3) = sod(121²), f(4) = sod(1212²), .... 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.

The first 16 terms are 1,9,16,36,40,54,55,72,79,90,94,108,118,126,133,144

For even numbered terms after 2 it appears f(n)=9n, but I only checked up to 16.
For the odd numbered terms the answer is in the vicinity of 9n, but mostly under.  The differences (-8,-2,-2,-8,-2,-5,+1,-2) don't show any apparent pattern.
 
Edit: the pattern for evens breaks down at 20
f(20)=171 = 9*19

Edited on March 3, 2014, 4:29 pm

Posted by Jer on 2014-03-03 16:26:12