查找C ++中偶数索引二项式系数的总和
考虑我们有一个数字n，我们必须找到偶数索引的二项式系数之和，例如$$\left（\begin{array}{c}n\\0\end{array}\right）+\left（\begin{array}{c}n\\2\end{array}\right）+\left（\begin{array}{c}n\\4\end{array}\right）+\left（\begin{array}{c}n\\6\end{array}\right）+...\left（\begin{array}{c}4\\0\end{array}\right）+\left（\begin{array}{c}4\\2\end{array}\right）+\left（\begin{array}{c}4\\4\end{array}\right）++=1+6+1=8$$
因此，这里我们将找到所有二项式系数，然后仅找到偶数索引值的总和。
示例
#include<iostream>
using namespace std;
int evenIndexedTermSum(int n) {
int coeff[n + 1][n + 1];
for (int i = 0; i <= n; i++) {
for (int j = 0; j <= min(i, n); j++) {
if (j == 0 || j == i)
coeff[i][j] = 1;
else
coeff[i][j] = coeff[i - 1][j - 1] + coeff[i - 1][j];
}
}
int sum = 0;
for (int i = 0; i <= n; i += 2)
sum += coeff[n][i];
return sum;
}
int main() {
int n = 8;
cout << "Sum of even placed binomial coefficients: " <<evenIndexedTermSum(n);
}输出结果
Sum of even placed binomial coefficients: 128
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