# Problem 242: Odd Triplets
Given the set {1,2,...,n}, we define f(n,k) as the number of its
k-element subsets with an odd sum of elements. For example, f(5,3) = 4,
since the set {1,2,3,4,5} has four 3-element subsets having an odd sum
of elements, i.e.: {1,2,4}, {1,3,5}, {2,3,4} and {2,4,5}. When all three
values n, k and f(n,k) are odd, we say that they make an odd-triplet
\[n,k,f(n,k)\]. There are exactly five odd-triplets with n ≤ 10, namely:
\[1,1,f(1,1) = 1\], \[5,1,f(5,1) = 3\], \[5,5,f(5,5) = 1\],
\[9,1,f(9,1) = 5\] and \[9,9,f(9,9) = 1\]. How many odd-triplets are
there with n ≤ 1012 ?