A beautiful geometric sequence!

Number Theory Level pending

The Sierpinski Triangle involves a sequence of geometric figures. The first figure in the sequence is an equilateral. The second has an inverted (white) equilateral inscribed inside an equilateral triangle as shown. Each subsequent figure in this sequence is obtained by inserting an inverted (white) triangle inside each non-inverted (shaded) triangle of the previous figure as shown above. How many regions ( both white and shaded together) are in the tenth figure in this sequence? For example, the first three figures in the sequence have 1 region, 4 regions and 13 regions respectively.

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