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.

Restricciones

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

Ejemplos

Entrada:
n = 3

Salida esperada:
expected = [0, 6, 28]

Entrada:
long long n = 3;

Salida esperada:
std::vector<long long> expected = {0, 6, 28};

Entrada:
long n = 3;

Salida esperada:
long[] expected = new long[] {0, 6, 28};

Entrada:
n = 1

Salida esperada:
expected = [0]

Entrada:
long long n = 1;

Salida esperada:
std::vector<long long> expected = {0};

Entrada:
long n = 1;

Salida esperada:
long[] expected = new long[] {0};

Referencias

Este reto está adaptado para CodeUtility. Sigue el enunciado y las restricciones indicadas arriba.

• Two Knights — 1072