infinite decimal number sequence.

1. 3 6 13 27 55 111 ...

All of these types of problems can be answered by a simple polynomial fit:

y=1720(n6+39n5325n4+1425n32194n2+2496n+720) < p easy if you think about it

first ten elements would be:

1,3,6,13,27,55,111,218,409,727,1224

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