%I #44 Jan 19 2023 11:11:44
%S 0,1,2,1,3,3,4,6,7,10,13,17,23,30,40,53,70,93,123,163,216,286,379,502,
%T 665,881,1167,1546,2048,2713,3594,4761,6307,8355,11068,14662,19423,
%U 25730,34085,45153,59815,79238,104968,139053,184206,244021,323259,428227
%N a(n) = a(n-2) + a(n-3).
%C Also the number of maximal matchings in the (n-2)-pan graph. - _Eric W. Weisstein_, Dec 30 2017
%H Vincenzo Librandi, <a href="/A007307/b007307.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Matching.html">Matching</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIndependentEdgeSet.html">Maximal Independent Edge Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PanGraph.html">Pan Graph</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1).
%F From _Wolfdieter Lang_, Jun 15 2010: (Start)
%F a(n) = p(n-1) + 2*p(n-2) = p(n+1) + p(n-2), with p(n):=A000931(n+3).
%F O.g.f: x*(1+2*x)/(1-x^2-x^3). (End)
%F a(n) = (A000931(n+1) + A001608(n+1))/2. - _Elmo R. Oliveira_, Dec 31 2022
%p G(x):=(-1-x^3)/(-1+x^2+x^3): f[0]:=G(x): for n from 1 to 58 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n]/n!,n=1..43); # _Zerinvary Lajos_, Mar 27 2009
%p # second Maple program:
%p a:= n-> (<<0|1|0>, <0|0|1>, <1|1|0>>^n.<<($0..2)>>)[1$2]:
%p seq(a(n), n=0..60); # _Alois P. Heinz_, Nov 06 2016
%t Table[- RootSum[-1 - # + #^3 &, -16 #^n - 13 #^(n + 1) + #^(n + 2) &]/23, {n, 20}] (* _Eric W. Weisstein_, Dec 30 2017 *)
%t LinearRecurrence[{0, 1, 1}, {1, 3, 3}, 20] (* _Eric W. Weisstein_, Dec 30 2017 *)
%t CoefficientList[Series[x (-1 - 3 x - 2 x^2)/(-1 + x^2 + x^3), {x, 0, 20}], x] (* _Eric W. Weisstein_, Dec 30 2017 *)
%o (Magma) I:=[0,1,2]; [n le 3 select I[n] else Self(n-2)+Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Jun 09 2013
%Y Cf. A000931, A001608.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_