The pattern described is a doubling of the number of pennies placed on each square of the chessboard.
- On the 1st square: \(2^0 = 1\) penny
- On the 2nd square: \(2^1 = 2\) pennies
- On the 3rd square: \(2^2 = 4\) pennies
- On the 4th square: \(2^3 = 8\) pennies
- On the 5th square: \(2^4 = 16\) pennies
- On the 6th square: \(2^5 = 32\) pennies
- On the 7th square: \(2^6 = 64\) pennies
- On the 8th square: \(2^7 = 128\) pennies
- On the 9th square: \(2^8 = 256\) pennies
- On the 10th square: \(2^9 = 512\) pennies
- On the 11th square: \(2^{10} = 1024\) pennies
- On the 12th square: \(2^{11} = 2048\) pennies
- On the 13th square: \(2^{12} = 4096\) pennies
- On the 14th square: \(2^{13} = 8192\) pennies
Thus, the number of pennies on the 14th square is 8,192 pennies.