OFFSET
1,2
COMMENTS
Also the number of maximal independent vertex sets (and minimal vertex covers) in the n-pan graph. - Eric W. Weisstein, Aug 07 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set
Eric Weisstein's World of Mathematics, Minimal Vertex Cover
Eric Weisstein's World of Mathematics, Pan Graph
Index entries for linear recurrences with constant coefficients, signature (0, 1, 1).
FORMULA
From Wolfdieter Lang, Jun 15 2010: (Start)
a(n) = p(n-1)+ 2*p(n) = p(n+2) + p(n), with p(n) = A000931(n+3) (Padovan); a(0)=2.
O.g.f.: (2 + x)/(1 - x^2 - x^3). (End)
MAPLE
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
MATHEMATICA
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 *)
LinearRecurrence[{0, 1, 1}, {1, 2, 3}, 50] (* Harvey P. Dale, Jul 14 2014 *)
Table[RootSum[-1 - # + #^3 &, 12 #^n + 4 #^(n + 1) + 5 #^(n + 2) &]/23, {n, 20}] (* Eric W. Weisstein, Aug 07 2017 *)
CoefficientList[Series[(-1 - 2 x - 2 x^2)/(-1 + x^2 + x^3), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 07 2017 *)
PROG
(Haskell)
a084338_list = [1, 2, 3] ++ zipWith (+) a084338_list (tail a084338_list)
a084338 n = a084338_list !! (n - 1)
-- Jack Willis, Dec 22 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 18 2003
EXTENSIONS
More terms from Erich Friedman, Aug 08 2005
STATUS
approved