what comes next in the sequence 6,12,20,32,52,88,156
factoring out a 2, we have
3,6,10,16,26,44,78
Not an easy polynomial, so it must be defined recursively.
6
12 = 2(6-0)
20 = 2(12-2)
32 = 2(20-4)
52 = 2(32-6)
88 = 2(52-8)
156 = 2(88-10)
So, it looks like
T0 = 6
Tn+1 = 2(Tn-2n)
So, the next term should be
2(156-12) = 288