输入一个数字，判断其是否为佩尔数，或输入N计算第N项佩尔数与总和。
佩尔数是一种特定的数列，定义为：佩尔数 \( P_n \) 由以下递推关系生成：
解答：
计算佩尔数列：
\( P_0 = 0 \)
\( P_1 = 1 \)
\( P_2 = 2P_1 + P_0 = 2 \times 1 + 0 = 2 \)
\( P_3 = 2P_2 + P_1 = 2 \times 2 + 1 = 5 \)
\( P_4 = 2P_3 + P_2 = 2 \times 5 + 2 = 12 \)
结果：
\( P_4 \) 已经超过 6 了，所以，6 不是佩尔数。
解答：
计算佩尔数列：
\( P_0 = 0 \)
\( P_1 = 1 \)
\( P_2 = 2P_1 + P_0 = 2 \times 1 + 0 = 2 \)
\( P_3 = 2P_2 + P_1 = 2 \times 2 + 1 = 5 \)
\( P_4 = 2P_3 + P_2 = 2 \times 5 + 2 = 12 \)
\( P_5 = 2P_4 + P_3 = 2 \times 12 + 5 = 29 \)
\( P_6 = 2P_5 + P_4 = 2 \times 29 + 12 = 70 \)
结果：
\( P_6 = 70 \)，所以，70 是佩尔数。
解答：
计算佩尔数列：
\( P_0 = 0 \)
\( P_1 = 1 \)
\( P_2 = 2P_1 + P_0 = 2 \times 1 + 0 = 2 \)
\( P_3 = 2P_2 + P_1 = 2 \times 2 + 1 = 5 \)
\( P_4 = 2P_3 + P_2 = 2 \times 5 + 2 = 12 \)
\( P_5 = 2P_4 + P_3 = 2 \times 12 + 5 = 29 \)
\( P_6 = 2P_5 + P_4 = 2 \times 29 + 12 = 70 \)
\( P_7 = 2P_6 + P_5 = 2 \times 70 + 29 = 169 \)
\( P_8 = 2P_7 + P_6 = 2 \times 169 + 70 = 408 \)
结果：
第 8 项佩尔数是 408，其总和为 696。