
COMMENTS

The Old Maid match is played with four players. For every game that is played, one of the four players is trolled at the end. The match ends when a player has been trolled three times, after which he loses the match.
So, to calculate the probability, we represent the four players by the digits 0, 1, 2, 3 in base 4 and then list out all the 18bit numbers in base 4.
Then A216074(n) = Number of numbers for which from the left, some digit has occurred three times at the nth position, i.e. 32 * a(n).
For four player match, the maximum number of games needed for a player to be trolled three times is 9. So, we consider with 9digit base 4 numbers.
Total value of A216074(i), for i = 3..9 is equal to 4^9 = 262144. (true chance)
Total value of a(i), for i = 3..9 is equal to 4^9/32 = 262144/32 = 8192.
gcd of A216074(i), for i = 3..9 is equal to 2^5 = 32.
The sequence A216074 gives the true number of ways for the match to last exactly for n games.
