Problem 28
Number spiral diagonals
Starting with the number $1$ and moving to the right in a clockwise direction, a $5$ by $5$ spiral is formed as follows:
20 7 8 9 10
19 6 1 2 11
18 5 4 3 12
17 16 15 14 13
It can be verified that the sum of the numbers on the diagonals is $101$.
What is the sum of the numbers on the diagonals in a $1001$ by $1001$ spiral formed in the same way?
螺旋数阵对角线
从$1$开始，按顺时针顺序铺开的$5 \times 5$螺旋数阵如下所示：
20 7 8 9 10
19 6 1 2 11
18 5 4 3 12
17 16 15 14 13
可以看出，该数阵对角线上的数之和是$101$。
考虑以同样方式构成的$1001 \times 1001$螺旋数阵，其对角线上的数之和是多少？