I wanted to know why a sequence like the above cannot be represented by a function. Is there any cue here?
Sorry for my lack of knowledge that such sequence can have a formula (or functions) generating the same. I am very indebted to all the comments and answers to opening my mind to such sequences being representable by a formula.
I request any source(s) (in book, or web-site, whatever) that asks such questions and gives good practice or theoretical basis.
The $n$th term in your sequence is $$ 4\frac{|n-1/2|}{n-1/2} + n $$
So it can be represented by a formula, if the formula is allowed to use absolute values.