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A276164 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.

%I A276164 #24 May 03 2025 07:44:43
%S A276164 1,2,4,7,10,15,17,26,27,40,38,57,52,77,67,100
%N A276164 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 A276164 a(2*n) = A005449(n) via [1, n+1, 2, n+2, ..., n, 2*n]
%D A276164 Peter Winkler, Mathematical Puzzles: A Connoisseur's Collection, A K Peters/CRC Press, 2003, pages 1-2.
%F A276164 a(n) = (A000217(n) + A276163(n))/2
%e A276164 a(1)  = 1  via [1]
%e A276164 a(2)  = 2  via [1,2]
%e A276164 a(3)  = 4  via [1,2,3]
%e A276164 a(4)  = 7  via [1,3,2,4]
%e A276164 a(5)  = 10 via [1,2,4,3,5]
%e A276164 a(6)  = 15 via [1,4,2,5,3,6]
%e A276164 a(7)  = 17 via [1,2,3,4,6,5,7]
%e A276164 a(8)  = 26 via [1,5,2,6,3,7,4,8]
%e A276164 a(9)  = 27 via [1,2,3,4,6,5,8,7,9]
%e A276164 a(10) = 40 via [1,6,2,7,3,8,4,9,5,10]
%e A276164 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 A276164 Cf. A276163.
%K A276164 more,nonn
%O A276164 1,2
%A A276164 _Peter Kagey_, Aug 22 2016
%E A276164 a(11)-a(16) from _Bert Dobbelaere_, May 03 2025