Two Nonattacking Knights

For each board size k from 1 through n, count unordered pairs of distinct squares on a k by k board where two knights cannot attack each other. A knight moves two squares in one axis and one in the other.

. x . x .
x . . . x
. . K . .
x . . . x
. x . x .

K marks a knight and x its possible destinations, when those squares lie on the board. Swapping the two knights does not create another placement.

Implement two_knights(n).

Input

n: The largest board size to consider.

Output

Return n counts in order, for board sizes 1 through n.

制約

1 ≤ n ≤ 10,000. Counts fit signed 64-bit integers.

例

入力：
n = 3

期待される出力：
expected = [0, 6, 28]

入力：
long long n = 3;

期待される出力：
std::vector<long long> expected = {0, 6, 28};

入力：
long n = 3;

期待される出力：
long[] expected = new long[] {0, 6, 28};

入力：
n = 1

期待される出力：
expected = [0]

入力：
long long n = 1;

期待される出力：
std::vector<long long> expected = {0};

入力：
long n = 1;

期待される出力：
long[] expected = new long[] {0};

参考資料

この課題はCodeUtility用に調整されています。上記の説明と制約に従ってください。

• Two Knights — 1072