We start the series with a,b,c,d as the first 4 terms.

The next 4 terms can be derived from the first 4 in the following way.

1. Place the last term(i.e d) as the first term of the new series.

2. The next terms of the new series are the next terms of the original series in a circular fashion (a,b,c,d,a,b,c,d....etc)

So the second set of terms is d,a,b,c.

In a similar way, the subsequent terms should be c,d,a,b and b,c,d,a.

The final series is a,b,c,d,d,a,b,c,c,d,a,b,b,c,d,a.