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 A216074 Number of ways in which a four-player Old Maid match lasts for exactly n games until a player has been trolled exactly three times. 1
 16384, 36864, 55296, 61440, 51840, 30240, 10080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS [From V. Raman, Dec 12 2012] (Start) 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 18-bit numbers in base 4. Then a(n) = Number of numbers for which from the left, some digit has occurred three times at the n-th position, i.e. 32 * A220017(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 9-digit base 4 numbers. Total value of a(i), for i = 3..9 is equal to 4^9 = 262144. Total value of A220017(i), for i = 3..9 is equal to 4^9/32 = 262144/32 = 8192. (relative chance) gcd of a(i), for i = 3..9 is equal to 2^5 = 32. The sequence A220017 gives the relative probability for the match to last exactly for n games. (End) LINKS FORMULA a(n) = 32 * A220017(n). CROSSREFS Cf. A220017 (relative probability). Sequence in context: A069415 A212936 A069275 * A258736 A255666 A220767 Adjacent sequences:  A216071 A216072 A216073 * A216075 A216076 A216077 KEYWORD nonn,fini,full AUTHOR V. Raman, Sep 01 2012 EXTENSIONS Edited by V. Raman, Dec 12 2012 STATUS approved

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Last modified October 25 17:22 EDT 2021. Contains 348255 sequences. (Running on oeis4.)