How many triangles are in the picture?

Question

Programming

How, knowing the length of the side of such a triangle, to find the number of triangles depicted (for the example above, the answer is 13)?

Answer 1

FOR DESCENDANTS: do not believe everything that is written on the Internet! this solution is wrong!
When the side of the triangle is increased by 1
C(i+1) =
C(i) /* all triangles of the previous figure (which has side i) */
+ 2i+1 /* triangles with side 1, drawn to one of the sides of the previous figure* /
+ i /* triangles with side 2 overlapping the previous one by 1 */
+ i-1 /* triangles with side 3 overlapping the previous one by 2*/
+ i-2 /* triangles with side 4 overlapping the previous one by 3*/
+ etc. up to zero (i.e. up to ii)

Answer 2

It is interesting to look at the graph of such dependence.

Answer 3

If you look for the answer in the form of a formula, then [n*(n+2)*(2*n+1)/8]
There, for even and odd n, different series are obtained, so you have to take the integer part (or be smart with (-1) ^n).