%I #20 Aug 25 2016 19:25:43
%S 1,2,4,7,10,15,17,26,27,40
%N a(n) is the maximum first-player score of a "Coins in a Row" game over all permutations of coins 1..n with both players using a minimax strategy.
%C a(2*n) = A005449(n) via [1, n+1, 2, n+2, ..., n, 2*n]
%D Peter Winkler, Mathematical Puzzles: A Connoisseur's Collection, A K Peters/CRC Press, 2003, pages 1-2.
%F a(n) = (A000217(n) + A276163(n))/2
%e a(1) = 1 via [1]
%e a(2) = 2 via [1,2]
%e a(3) = 4 via [1,2,3]
%e a(4) = 7 via [1,3,2,4]
%e a(5) = 10 via [1,2,4,3,5]
%e a(6) = 15 via [1,4,2,5,3,6]
%e a(7) = 17 via [1,2,3,4,6,5,7]
%e a(8) = 26 via [1,5,2,6,3,7,4,8]
%e a(9) = 27 via [1,2,3,4,6,5,8,7,9]
%e a(10) = 40 via [1,6,2,7,3,8,4,9,5,10]
%e For n=4, the first player would take 4, the second player would take 2, the first player would take 3, and the second player would take 1. The first player's resulting score would be 4 + 3 = 7.
%Y Cf. A276163.
%K more,nonn
%O 1,2
%A _Peter Kagey_, Aug 22 2016