This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A279673 #22 Sep 08 2022 08:46:18
%S A279673 1,3,9,19,41,99,233,531,1225,2851,6601,15251,35305,81763,189225,
%T A279673 437907,1013641,2346275,5430537,12569363,29093289,67339363,155862889,
%U A279673 360759571,835013705,1932719395,4473463369,10354262163,23965938537,55471468387,128394046889
%N A279673 The maximum number of coins that can be processed in n weighings where all coins are real except for one LHR-coin starting in the light state.
%C A279673 An LHR-coin is a coin that can change its weight periodically from light to heavy to real to light.
%C A279673 If an LHR-coin starts in the real state, then the maximum number of coins that can be processed in n weighings is a(n-1).
%C A279673 Also the number of outcomes of n weighings such that every even-numbered imbalance that is not the last one must be followed by a balance.
%H A279673 Colin Barker, <a href="/A279673/b279673.txt">Table of n, a(n) for n = 0..1000</a>
%H A279673 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 A279673 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,4).
%F A279673 a(n) = 2a(n-1) - a(n-2) + 4a(n-3).
%F A279673 G.f.: (1 + x + 4*x^2) / (1 - 2*x + x^2 - 4*x^3). - _Colin Barker_, Dec 17 2016
%e A279673 If we have three weighings we are not allowed to have outcomes that consist of three imbalances. That means a(3) = 27 - 8 = 19.
%e A279673 If we have four weighings we are not allowed the following outcomes: =<<<, <=<<, <<<=, <<<<, where any less-than sign can be interchanged with a greater-than sign. Thus a(4) = 81 - 3*8 - 16 = 41.
%t A279673 LinearRecurrence[{2, -1, 4}, {1, 3, 9}, 30]
%o A279673 (Magma) I:=[1,3,9]; [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
%o A279673 (PARI) Vec((1 + x + 4*x^2) / (1 - 2*x + x^2 - 4*x^3) + O(x^40)) \\ _Colin Barker_, Dec 17 2016
%Y A279673 Cf. A279674, A279682, A279684, A279685.
%K A279673 nonn,easy
%O A279673 0,2
%A A279673 _Tanya Khovanova_ and _Konstantin Knop_, Dec 16 2016