

A247160


Dynamic Betting Game D(n,4,3).


9



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80
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OFFSET

1,2


COMMENTS

Players A and B bet in a kround 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 = 4 and r = 3. Note that with a(0)=0, a(n+1)a(n) is a periodic function of n with value = 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2.


LINKS

Charles JwoYue Lien, Dynamic Betting Game, Southeast Asian Bulletin of Mathematics, 2015, Vol. 39 Issue 6, pp. 799814.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1).


FORMULA

a(n) = floor(n*16/15).
a(n) = a(n1) + a(n15)  a(n16).  Colin Barker, Sep 11 2014
G.f.: x*(2*x^14 +x^13 +x^12 +x^11 +x^10 +x^9 +x^8 +x^7 +x^6 +x^5 +x^4 +x^3 +x^2 +x +1) / ((x 1)^2*(x^2 +x +1)*(x^4 +x^3 +x^2 +x +1)*(x^8 x^7 +x^5 x^4 +x^3 x +1)).  Colin Barker, Sep 11 2014


PROG

(Haskell)
a247160 n = a247160_list !! (n1)
a247160_list = [1..14] ++ [16, 17] ++ zipWith (+)
(drop 15 a247160_list) (zipWith () (tail a247160_list) a247160_list)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



