I want to know the formula for the general term of the following recurrence system. I guess it can be written with `Floor` or `Mod`. How can I find it?

```
RSolve[{a[n + 5] == a[n] + 6, a[1] == 1, a[2] == 3, a[3] == 2, a[4] == 1, a[5] == 1}, a[n], n]

DiscretePlot[-2 + (6 n)/5 + 
  2/5 Sqrt[28 + 53/Sqrt[5]] Sin[(2 n π)/5 - ArcTan[15/Sqrt[85 + 38 Sqrt[5]]]] + 
  2/5 Sqrt[28 - 53/Sqrt[5]] Sin[(4 n π)/5 - ArcTan[3 Sqrt[5 (85 + 38 Sqrt[5])]]],
 {n, 1, 20}]

```

**Updated**

I would like to have the formula for the general term without using recursion just as

```
RecurrenceTable[{y[n + 5] == y[n] + 1, 
  Sequence @@ Table[y[i] == i, {i, 5}]}, y, {n, 1, 30}]

```

can be written 

```
n - 4 Floor[(n - 1)/5] /. n -> Range@30

```