At the beginning of the first day, the box contains 1 black ball and 1 gold ball. At the end of the first day, 2 black balls and 1 gold ball are added, so the box contains 3 black balls and 2 gold balls. At the end of the second day, $2 \times 2=4$ black balls and $2 \times 1=2$ gold balls are added, so the box contains 7 black balls and 4 gold balls. Continuing in this way, we find the following numbers of balls: End of Day 2: 7 black balls, 4 gold balls; End of Day 3: 15 black balls, 8 gold balls; End of Day 4: 31 black balls, 16 gold balls; End of Day 5: 63 black balls, 32 gold balls; End of Day 6: 127 black balls, 64 gold balls; End of Day 7: 255 black balls, 128 gold balls. At the end of the 7th day, there are thus 255+128=383 balls in the box.
At the beginning of the first day, a box contains 1 black ball, 1 gold ball, and no other balls. At the end of each day, for each gold ball in the box, 2 black balls and 1 gold ball are added to the box. If no balls are removed from the box, how many balls are in the box at the end of the seventh day?