196 (number)

In mathematics

196 is a square number, the square of 14. As the square of a Catalan number, it counts the number of walks of length 8 in the positive quadrant of the integer grid that start and end at the origin, moving diagonally at each step. It is part of a sequence of square numbers beginning 0, 1, 4, 25, 196, ... in which each number is the smallest square that differs from the previous number by a triangular number.

There are 196 one-sided heptominoes, the polyominoes made from 7 squares. Here, one-sided means that asymmetric polyominoes are considered to be distinct from their mirror images.

A Lychrel number is a natural number which cannot form a palindromic number through the iterative process of repeatedly reversing its digits and adding the resulting numbers. 196 is the smallest number conjectured to be a Lychrel number in base 10; the process has been carried out for over a billion iterations without finding a palindrome, but no one has ever proven that it will never produce one.{{cite journal

References

References

1. {{cite OEIS. A001246. Squares of Catalan numbers
2. {{cite OEIS. A036449. Values square, differences triangular
3. {{cite OEIS. A000988. Number of one-sided polyominoes with n cells
4. {{cite OEIS. A023108. A023108