A366996 a(n) is the denominator of the expected end time of a game with three gamblers, one of which starts with capital n, the others with capital 1 each, conditional on the event that one of the two poor players wins.

1, 7, 41, 197, 7025, 68761, 1663251, 178945525, 132150155017, 16077043550231, 4833128874789907, 250487901809049775, 6590569678028479808009, 30288529373611329886681, 111694000110134843095617996833, 2161868815213291879136716036071, 7842015457241561891262053489240216057

Offset

1,2

Comments

In each round of the game, 1 unit is transferred from one randomly chosen player to another. Players play until they are out of money, so when the first player is out the other two continue to play. The winner is the player who ends up with all n+2 units of money.

See A366995 for references and programs.

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..53

Crossrefs

Cf. A366566 (A366995(n)/a(n) rounded to nearest integer), A366995 (numerators).

Sequence in context: A034575 A237854 A219862 * A238991 A084779 A266887

Adjacent sequences: A366993 A366994 A366995 * A366997 A366998 A366999

Keyword

nonn,frac

Author

Pontus von Brömssen, Oct 31 2023

Status

approved