%I #15 Apr 24 2017 00:29:34
%S 0,1,4,10,26,64,160,396,984,2440,6056,15024,37280,92496,229504,569440,
%T 1412896,3505664,8698240,21582016,53549184,132865920,329666176,
%U 817965824,2029532160,5035663616,12494459904,31001182720,76919958016,190853361664,473544273920,1174955355136,2915292534784
%N Expansion of (x+2*x^2) / (1-2*x-2*x^2+2*x^3).
%H Colin Barker, <a href="/A285186/b285186.txt">Table of n, a(n) for n = 0..1000</a>
%H Tomislav Doslic, I. Zubac, <a href="http://amc-journal.eu/index.php/amc/article/view/851">Counting maximal matchings in linear polymers</a>, Ars Mathematica Contemporanea 11 (2016) 255-276. See Prop. 4.11.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-2).
%F a(n) = A285185(n)/2.
%F a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) for n>2. - _Colin Barker_, Apr 23 2017
%o (PARI) concat(0, Vec(x*(1 + 2*x) / (1 - 2*x - 2*x^2 + 2*x^3) + O(x^30))) \\ _Colin Barker_, Apr 23 2017
%Y Cf. A285185.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Apr 23 2017