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A279674
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The maximum number of coins that can be processed in n weighings that all are real except for one LHR-coin starting in the heavy state.
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6
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1, 3, 5, 11, 29, 67, 149, 347, 813, 1875, 4325, 10027, 23229, 53731, 124341, 287867, 666317, 1542131, 3569413, 8261963, 19123037, 44261763, 102448341, 237127067, 548852845, 1270371987, 2940399397, 6805838187, 15752764925, 36461289251, 84393166325, 195336103099
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OFFSET
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0,2
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COMMENTS
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An LHR-coin is a coin that can change its weight periodically from light to heavy to real to light.
Also the number of outcomes of n weighings such that every odd-numbered imbalance that is not the last one must be followed by a balance.
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LINKS
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FORMULA
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a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3).
G.f.: (1 + x) / (1 - 2*x + x^2 - 4*x^3). - Colin Barker, Dec 17 2016
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EXAMPLE
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If we have two weighings we are not allowed to have outcomes that consist of two imbalances. That means a(2) = 9 - 4 = 5.
If we have three weighings we are not allowed the following outcomes: =<<, <<=, <<<, where any less-than sign can be interchanged with a greater-than sign. Thus a(3) = 27 - 2*4 - 8 = 11.
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MATHEMATICA
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LinearRecurrence[{2, -1, 4}, {1, 3, 5}, 30]
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PROG
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(Magma) I:=[1, 3, 5]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-2)+4*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Dec 17 2016
(PARI) Vec((1 + x) / (1 - 2*x + x^2 - 4*x^3) + O(x^40)) \\ Colin Barker, Dec 17 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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