Can anyone please help me find a formula for this sequence:

4, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12...

It's based on fewest number of 2-blocks required to surround an increasing number of 1-blocks.

I've tried the method where you find differences between terms (up to 6 columns worth), but cannot get it to resolve to one value. Does this mean that it isn't quadratic?

Tried using Excel to find a line of best fit and a 'moving average' line fits really well. Still didn't help me derive a formula.

Any help would be greatly appreciated!