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.

Vincoli

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

Esempi

Input:
n = 3

Output atteso:
expected = [0, 6, 28]

Input:
long long n = 3;

Output atteso:
std::vector<long long> expected = {0, 6, 28};

Input:
long n = 3;

Output atteso:
long[] expected = new long[] {0, 6, 28};

Input:
n = 1

Output atteso:
expected = [0]

Input:
long long n = 1;

Output atteso:
std::vector<long long> expected = {0};

Input:
long n = 1;

Output atteso:
long[] expected = new long[] {0};

Riferimenti

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• Two Knights — 1072