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Expansion of (x+2*x^2) / (1-2*x-2*x^2+2*x^3).
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%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