Solve Sequence to find next six numbers

I have a sequence to solve and get the next six numbers. I have all the stats for the data like 1st difference, second difference, third difference, mean, median, variance...

Sequence: 0,1,2,1,0,1,0,3,0,1,0,3,2,1,2,3

Answer 1

[Ajay Kumar]

The next six numbers are

2 3 0 3 2 3

Now the starting point element/vector is

A = [0 1 2 1 0 1 0 3 0 1 0 3 2 1 2 3 2 3 0 3 2 3];

(note that if A1=A(1:11) and A2 = A(12:22), then A1 + A2 = 3 * ones(1,11))

If we start with A3 = A, then we have a recursive formula An=[A(n-1) 3-A(n-1)]

Credit: Roman Dyba, Mountain View CA

Answer 2

[Walter Roberson]

The next 6 numbers in the sequence are all 19. This was proven by Carl E. Linderholm in his paper Mathematics Made Difficult.