(*
The sum of the squares of the first ten natural numbers is,
1^(2) + 2^(2) + ... + 10^(2) = 385

The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)^(2) = 55^(2) = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 ? 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
*)

let dsq l =
  let rec dsq l =
    match l with
    [] -> 0
    | h::t ->
      ( List.fold_left (+) 0 ( List.map ( fun x->(h*x) ) t ) )+
      ( dsq t )
  in
    2*(dsq l)
;;

(* list nat numbers below n *)
let nb n =
  let rec pdb n l =
    if (n<1) 
    then l
    else pdb (n-1) (n::l)
  in
    pdb n []
;;

Printf.printf "%d\n" (dsq (nb 100));;