Originally Posted by

**Plato** As you can see I fixed the subscripts using {} \$a_n = a_{n-1} + a_{n-3}\$ Any time you have a superscript or subscript with more than one character in it enclose the whole superscript or subscript in braces.

Please review the post for mistakes. You post $a_n = a_{n-1} + \color{red}{a_{n-3}}$ and its base case is $a_1 = 1 \ a_2 = 2 \ a_3 = 3$ Is that correct?

Because that means $a_4=4,a_5=6,a_6=9,a_7=13,a_8=19,a_9=28,a_{10}=41$ There is nothing wrong with the recursion. But it does not go with this phrase "every natural number can be written as a sum (of one or more) of different elements of the series $a_n$"

Maybe you can give a clearer explanation of what it means? Please do!