OFFSET
1,2
COMMENTS
Players A and B bet in a k-round game. Player A has an initial amount of money n. In each round, player A can wager an integer between 0 and what he has. Player A then gains or loses an amount equal to his wager depending on whether player B lets him win or lose. Player B tries to minimize player A's money at the end. The number of rounds player A can lose is r. a(n) is the maximum amount of money player A can have at the end of the game for k = 5 and r = 3.
LINKS
Charles Jwo-Yue Lien, Dynamic Betting Game, Southeast Asian Bulletin of Mathematics, 2015, Vol. 39 Issue 6, pp. 799-814.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,1,-1).
FORMULA
With a(0)=0, a(n+1)-a(n) is a periodic function of n with value = 1,1,1,1,1,1,2,1,1,1,1,1,3.
a(n) = a(n-1) + a(n-13) - a(n-14). - Colin Barker, Sep 11 2014
G.f.: x*(3*x^12 +x^11 +x^10 +x^9 +x^8 +x^7 +2*x^6 +x^5 +x^4 +x^3 +x^2 +x +1) / ((x -1)^2*(x^12 +x^11 +x^10 +x^9 +x^8 +x^7 +x^6 +x^5 +x^4 +x^3 +x^2 +x +1)). - Colin Barker, Sep 11 2014
EXAMPLE
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Charles Jwo-Yue Lien, Sep 10 2014
STATUS
approved