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 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 (list; graph; refs; listen; history; text; internal format)
 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 = 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 Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 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 (1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1). FORMULA a(n) = floor(n*16/15). a(n) = a(n-1) + a(n-15) - a(n-16). - 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 !! (n-1) a247160_list = [1..14] ++ [16, 17] ++ zipWith (+) (drop 15 a247160_list) (zipWith (-) (tail a247160_list) a247160_list) -- Reinhard Zumkeller, Sep 19 2014 CROSSREFS Cf. A247060, A247061, A247062, A247063, A247064, A247161. Sequence in context: A187829 A356974 A105427 * A023808 A331995 A347457 Adjacent sequences: A247157 A247158 A247159 * A247161 A247162 A247163 KEYWORD nonn,easy AUTHOR Charles Jwo-Yue Lien, Sep 10 2014 EXTENSIONS Typo in data fixed by Colin Barker, Sep 11 2014 STATUS approved

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