There is a sequence 1 - 2 - 3 4 - 5 - 6 7 - 8 - 9 10 - 11 - 12 13?

There is a sequence 1 - 2 - 3 4 - 5 - 6 7 - 8 - 9 10 - 11 - 12 13?

The sequence consists of
It is determined by the positive and negative coefficients of 1-1-11-1-1.3 cycles, so we only need to construct this cycle
Divide by 3 and take the remainder to construct
as
6 / 3 over 0, remember 6 mod 3 = 0
7 / 3 more than 1, remember 7 Mod 3 = 1
8 / 3 more than 2 remember 8 mod 3 = 2
9 / 3 over 1, remember 9 mod 3 = 0
10 / 3 over 0 remember 10 mod 3 = 1
11 / 3 more than 1, remember 11 mod 3 = 2
.
So an = n when n + 2 mod 3 = 0
An = - n when n + 2 mod 3 = 1
An = - n when n + 2 mod 3 = 2
When you arrange the sequence into two dimensions, you have a variable, a transverse x and a longitudinal y, as follows
1 -2 -3
4 -5 -6
7 -8 -9
10 -11 -12
.
Obviously, y = 3n-1, x = B (3n-1 + a) (a belongs to 0,1,2, B belongs to 1, - 1, - 1; n belongs to natural number)
An = (y, x) this type can be solved in this way, for example
Yang Hui series
one
1 1
1 2 1
1 3 3 1
.
such as
1;
1,1;
1,2,2,2,1;
1,3,5,7,8,8,8,8,7,5,3,1;
1,4,9,16,24,32,40,48,55,60,63,64,64,64,64,
.