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%I #33 Aug 07 2017 23:13:14
%S 1,2,3,3,5,6,8,11,14,19,25,33,44,58,77,102,135,179,237,314,416,551,
%T 730,967,1281,1697,2248,2978,3945,5226,6923,9171,12149,16094,21320,
%U 28243,37414,49563,65657,86977,115220,152634,202197,267854,354831
%N a(1) = 1, a(2) = 2, a(3) = 3, a(n+3) = a(n) + a(n+1).
%C Also the number of maximal independent vertex sets (and minimal vertex covers) in the n-pan graph. - _Eric W. Weisstein_, Aug 07 2017
%H Vincenzo Librandi, <a href="/A084338/b084338.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIndependentVertexSet.html">Maximal Independent Vertex Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalVertexCover.html">Minimal Vertex Cover</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) = p(n+2) + p(n), with p(n) = A000931(n+3) (Padovan); a(0)=2.
%F O.g.f.: (2 + x)/(1 - x^2 - x^3). (End)
%p G(x):=(-1-x^2)/(-1+x^2+x^3): f[0]:=G(x): for n from 1 to 60 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n+2]/(n+2)!, n=1..50); # _Zerinvary Lajos_, Mar 27 2009
%t Join[{a=1,b=2,c=3},Table[d=a+b;a=b;b=c;c=d,{n,100}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 26 2011 *)
%t LinearRecurrence[{0, 1, 1}, {1, 2, 3}, 50] (* _Harvey P. Dale_, Jul 14 2014 *)
%t Table[RootSum[-1 - # + #^3 &, 12 #^n + 4 #^(n + 1) + 5 #^(n + 2) &]/23, {n, 20}] (* _Eric W. Weisstein_, Aug 07 2017 *)
%t CoefficientList[Series[(-1 - 2 x - 2 x^2)/(-1 + x^2 + x^3), {x, 0, 20}], x] (* _Eric W. Weisstein_, Aug 07 2017 *)
%o (Haskell)
%o a084338_list = [1,2,3] ++ zipWith (+) a084338_list (tail a084338_list)
%o a084338 n = a084338_list !! (n - 1)
%o -- _Jack Willis_, Dec 22 2013
%K nonn,easy
%O 1,2
%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 18 2003
%E More terms from _Erich Friedman_, Aug 08 2005
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