The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A276168 a(n) is the minimum first-player score difference of a "Coins in a Row" game over all permutations of coins 1..n with both players using a minimax strategy. 1
 1, 1, 0, 0, -3, 1, -8, 0, -15, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS A positive value indicates that all permutations of 1..n result in a game where the first player has a winning strategy. A negative value indicates that there exists a permutation of 1..n where the second player has a winning strategy. a(2*k) is strictly nonnegative. Conjecture: a(2*n - 1) = -A067998(n). Conjecture: a(n) = n + 1 - A276163(n + 1) for all n >= 1. REFERENCES Peter Winkler, Mathematical Puzzles: A Connoisseur's Collection, A K Peters/CRC Press, 2003, pages 1-2. LINKS EXAMPLE a(1) = 1;   via [1] a(2) = 1;   via [1,2] a(3) = 0;   via [1,3,2] a(4) = 0;   via [1,2,4,3] a(5) = -3;  via [1,4,2,5,3] a(6) = 1;   via [1,2,3,4,6,5] a(7) = -8;  via [1,5,2,6,3,7,4] a(8) = 0;   via [1,2,3,4,6,5,8,7] a(9) = -15; via [1,6,2,7,3,8,4,9,5] PROG (Haskell) minimax [] = 0 minimax as = max (head as - minimax (tail as)) (last as - minimax (init as)) a276168 n = minimum \$ map minimax \$ permutations [1..n] CROSSREFS Cf. A276163. Sequence in context: A096797 A084246 A141252 * A165498 A195731 A331187 Adjacent sequences:  A276165 A276166 A276167 * A276169 A276170 A276171 KEYWORD sign,more AUTHOR Peter Kagey, Aug 29 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 15 23:24 EDT 2021. Contains 343937 sequences. (Running on oeis4.)