-- Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
--
-- Triangle    T[n]=n(n+1)/2   1, 3,  6, 10, 15, ...
-- Pentagonal  P[n]=n(3n−1)/2  1, 5, 12, 22, 35, ...
-- Hexagonal   H[n]=n(2n−1)    1, 6, 15, 28, 45, ...
--
-- It can be verified that T[285] = P[165] = H[143] = 40755.
--
-- Find the next triangle number that is also pentagonal and hexagonal.

import Euler

triangles, pentagonals, hexagonals :: [Int]
triangles   = map (\n -> n*(n+1) `div` 2) [1..]
pentagonals = map (\n -> n*(3*n-1) `div` 2) [1..]
hexagonals  = map (\n -> n*(2*n-1)) [1..]

main = print $ go triangles pentagonals $ dropWhile (<= 40755) hexagonals
   where
      go ts@(t:_) ps@(p:_) hs@(h:_)
         | (t == p) && (t == h) = t
         | h < t || h < p = go ts ps (tail hs)
         | otherwise = go (dropWhile (< h) ts) (dropWhile (< h) ps) hs