题目242：奇数三元组
Odd TripletsGiven 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 .
There are exactly five odd-triplets with n ≤ 10, namely:
, , , and .
How many odd-triplets are there with n ≤ 1012 ?
题目：
给定集合 {1,2,...,n}，定义 f(n,k) 为其元素和为奇数的 k 元子集的数目。例如，f(5,3) = 4，因为集合 {1,2,3,4,5} 有 4 个元素和为奇数的 3 元子集：{1,2,4}, {1,3,5}, {2,3,4} 和 {2,4,5}。
当 n, k 和 f(n,k) 的值均为奇数时，我们称它们构成奇数三元组 。
当 n ≤ 10 时有 5 个奇数三元组，也就是：
，， 和 。
当 n ≤ 1012 时有多少个奇数三元组？
页:
[1]