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A276167 a(n) is the second player's score in a "Coins in a Row" game over the n-th row of A066099 using a minimax strategy.

%I A276167 #17 Aug 27 2016 02:11:16
%S A276167 0,0,0,1,0,1,1,1,0,1,2,1,1,2,1,2,0,1,2,1,2,2,2,2,1,3,2,2,1,2,2,2,0,1,
%T A276167 2,1,3,2,2,2,2,3,2,3,2,2,3,2,1,4,3,2,2,3,2,3,1,2,3,3,2,3,2,3,0,1,2,1,
%U A276167 3,2,2,2,3,3,2,3,3,2,3,2,2,4,3,3,2,3,3
%N A276167 a(n) is the second player's score in a "Coins in a Row" game over the n-th row of A066099 using a minimax strategy.
%C A276167 "Coins in a Row" is a game in which players alternate picking up coins of varying denominations from the end of the row in an attempt to collect as many points as possible.
%D A276167 Peter Winkler, Mathematical Puzzles: A Connoisseur's Collection, A K Peters/CRC Press, 2003, pages 1-2.
%H A276167 Peter Kagey, <a href="/A276167/b276167.txt">Table of n, a(n) for n = 0..10000</a>
%F A276167 a(n) = A029837(n + 1) - A276166(n).
%F A276167 a(n) = A276166(n) - A276165(n).
%e A276167 Let [R,L,L,L] represent a game in which the first player takes the right coin, the second player takes the left coin, the first player takes the left coin, and the second player takes the left (only remaining) coin.
%e A276167 A066099_Row(0)    = [0];         a(0)    = 0 via [L]
%e A276167 A066099_Row(1)    = [1];         a(1)    = 0 via [L]
%e A276167 A066099_Row(3)    = [1,1];       a(3)    = 1 via [R,L]
%e A276167 A066099_Row(22)   = [2,1,2];     a(22)   = 2 via [L,R,L]
%e A276167 A066099_Row(88)   = [2,1,4];     a(88)   = 2 via [R,L,L]
%e A276167 A066099_Row(1418) = [2,1,4,2,2]; a(1418) = 6 via [L,R,R,R,L]
%o A276167 (Haskell)
%o A276167 minimaxDifference [] = 0
%o A276167 minimaxDifference as = max (head as - minimaxDifference (tail as)) (last as - minimaxDifference (init as))
%o A276167 minimaxScore2 as = (sum as - minimaxDifference as) `div` 2
%o A276167 a276167 = minimaxScore2 . a066099_row
%Y A276167 Cf. A276163, A276164, A276165, A276166.
%K A276167 nonn
%O A276167 0,11
%A A276167 _Peter Kagey_, Aug 25 2016