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 A276166 a(n) is the first player's score in a "Coins in a Row" game over the n-th row of A066099 using a minimax strategy. 3
 0, 1, 2, 1, 3, 2, 2, 2, 4, 3, 2, 3, 3, 2, 3, 2, 5, 4, 3, 4, 3, 3, 3, 3, 4, 2, 3, 3, 4, 3, 3, 3, 6, 5, 4, 5, 3, 4, 4, 4, 4, 3, 4, 3, 4, 4, 3, 4, 5, 2, 3, 4, 4, 3, 4, 3, 5, 4, 3, 3, 4, 3, 4, 3, 7, 6, 5, 6, 4, 5, 5, 5, 4, 4, 5, 4, 4, 5, 4, 5, 5, 3, 4, 4, 5, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS "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. REFERENCES Peter Winkler, Mathematical Puzzles: A Connoisseur's Collection, A K Peters/CRC Press, 2003, pages 1-2. LINKS Peter Kagey, Table of n, a(n) for n = 0..10000 FORMULA a(n) = A029837(n + 1) - A276167(n). a(n) = A276165(n) + A276167(n). EXAMPLE 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. A066099_Row(0)    = [0];         a(0)    = 0 via [L] A066099_Row(1)    = [1];         a(1)    = 1 via [L] A066099_Row(3)    = [1,1];       a(3)    = 1 via [R,L] A066099_Row(22)   = [2,1,2];     a(22)   = 3 via [L,R,L] A066099_Row(88)   = [2,1,4];     a(88)   = 5 via [R,L,L] A066099_Row(1418) = [2,1,4,2,2]; a(1418) = 5 via [L,R,R,R,L] PROG (Haskell) minimaxDifference [] = 0 minimaxDifference as = max (head as - minimaxDifference (tail as)) (last as - minimaxDifference (init as)) minimaxScore as = (sum as + minimaxDifference as) `div` 2 a276166 = minimaxScore . a066099_row CROSSREFS Cf. A276163, A276164, A276165, A276167. Sequence in context: A035191 A297167 A303389 * A177062 A133924 A023135 Adjacent sequences:  A276163 A276164 A276165 * A276167 A276168 A276169 KEYWORD nonn AUTHOR Peter Kagey, Aug 25 2016 STATUS approved

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Last modified January 19 04:09 EST 2019. Contains 319304 sequences. (Running on oeis4.)