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A004278
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1, 3 and the positive even numbers.
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3
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1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104
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OFFSET
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1,2
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COMMENTS
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a(n) is the maximum number of turns that player A needs to identify with certainty the location of the coin that player B has hidden in one box in a row of n + 1 boxes. Player A starts by opening one of the boxes to see if the coin is in that box. After that, B secretly relocates the coin from its current box to one of the neighboring boxes, except when n = 1. In that case the game ends before B can relocate the coin. On each turn player A opens one box and when player A can tell in which box the coin is located, the game ends. Can be proved. - Bob Andriesse, Dec 22 2017
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LINKS
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FORMULA
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G.f.: (x + x^5)/(1 - x)^2.
a(n) = 2*a(n-1) - a(n-2), n > 2 and n is not 5.
a(n) = 2*n - 2 + floor((4/Pi)*arctan(2 - n)).
(End)
E.g.f.: 2*e^x*(x - 1) + 3 + 2*x + x^2/2. - Iain Fox, Dec 22 2017
a(n) = (abs(4 - n) + 3*n - 4)/2. - Iain Fox, Dec 23 2017
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MATHEMATICA
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PROG
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(Haskell)
a004278 n = if n <= 3 then n else 2 * (n - 2)
a004278_list = [1, 2, 3] ++ [4, 6 ..]
(PARI) first(n) = Vec((x + x^5)/(x - 1)^2 + O(x^(n+1))) \\ Iain Fox, Dec 21 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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