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.

सीमाएँ

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

उदाहरण

इनपुट:
n = 3

अपेक्षित आउटपुट:
expected = [0, 6, 28]

इनपुट:
long long n = 3;

अपेक्षित आउटपुट:
std::vector<long long> expected = {0, 6, 28};

इनपुट:
long n = 3;

अपेक्षित आउटपुट:
long[] expected = new long[] {0, 6, 28};

इनपुट:
n = 1

अपेक्षित आउटपुट:
expected = [0]

इनपुट:
long long n = 1;

अपेक्षित आउटपुट:
std::vector<long long> expected = {0};

इनपुट:
long n = 1;

अपेक्षित आउटपुट:
long[] expected = new long[] {0};

संदर्भ

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• Two Knights — 1072