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A279685 The maximum number of coins that can be processed in n weighings of an adaptive strategy that all are real (and identical) except for one LHR-coin starting in an unknown state.

%I A279685 #21 Dec 21 2016 11:07:21
%S A279685 1,1,3,6,16,39,91,216,499,1144,2651,6152,14227,32904,76187,176376,
%T A279685 408179,944728,2186779,5061544,11715219,27116008,62762971,145270808,
%U A279685 336242675,778266424,1801373403,4169451080,9650594451,22337231432,51701672731
%N A279685 The maximum number of coins that can be processed in n weighings of an adaptive strategy that all are real (and identical) except for one LHR-coin starting in an unknown state.
%C A279685 An LHR-coin is a coin that can change its weight periodically from light to heavy to real to light.
%H A279685 Colin Barker, <a href="/A279685/b279685.txt">Table of n, a(n) for n = 0..1000</a>
%H A279685 Tanya Khovanova and Konstantin Knop, <a href="https://arxiv.org/abs/1611.09201">Coins that Change Their Weights</a>, arXiv:1611.09201 [math.CO], 2016.
%H A279685 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,5,-4).
%F A279685 a(n) = (A279673(n-1) + 1)/2 + A279673(n-2), for n > 6.
%F A279685 From _Colin Barker_, Dec 17 2016: (Start)
%F A279685 a(n) = 3*a(n-1) - 3*a(n-2) + 5*a(n-3) - 4*a(n-4) for n>9.
%F A279685 G.f.: (1 - 2*x + 3*x^2 - 5*x^3 + 6*x^4 - 2*x^5 + 4*x^6 + 4*x^7 - 7*x^8 - 4*x^9) / ((1 - x)*(1 - 2*x + x^2 - 4*x^3)).
%F A279685 (End)
%o A279685 (PARI) Vec((1 - 2*x + 3*x^2 - 5*x^3 + 6*x^4 - 2*x^5 + 4*x^6 + 4*x^7 - 7*x^8 - 4*x^9) / ((1 - x)*(1 - 2*x + x^2 - 4*x^3)) + O(x^40)) \\ _Colin Barker_, Dec 17 2016
%Y A279685 Cf. A279673, A279674, A279682, A279684.
%K A279685 nonn,easy
%O A279685 0,3
%A A279685 _Tanya Khovanova_ and _Konstantin Knop_, Dec 16 2016