# Jesse's path

A 18 mile by 57 mile plot of land is divided into $$1026$$ counties of 1 mile by 1 mile squares. A man starts at the top right corner of the plot and travels a straight line path to the bottom left corner. In each county that he travels through, he spends $$-4$$ times the sum of the amounts he spent in the previous two counties. He spends $1 in the first county and$2 in the second county. If he spends $$a\times 2^b$$ dollars in the last county, where $$a$$ is odd and $$b \geq 0$$, find $$a+b$$.

This problem is posed by Jesse Z.

Details and assumptions

Spending a negative amount of money is equivalent to receiving money. As an explicit example, he receives \$12 in the third county.

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