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A279674 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. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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.
LINKS
Tanya Khovanova and Konstantin Knop, Coins that Change Their Weights, arXiv:1611.09201 [math.CO], 2016.
FORMULA
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
EXAMPLE
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.
MATHEMATICA
LinearRecurrence[{2, -1, 4}, {1, 3, 5}, 30]
PROG
(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
CROSSREFS
Sequence in context: A328329 A326392 A213210 * A194563 A080443 A168607
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 04:05 EDT 2024. Contains 371235 sequences. (Running on oeis4.)