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.
The original sub was r/195, as it was started by roommates whose room number was 195. Then later for whatever reason appeared the spinoff r/196 and got more popular than the original.
Like I'm 80% sure that this is how it happened and that it's not semi-made-up by myself because I misremember the story...
