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 A084338 a(1) = 1, a(2) = 2, a(3) = 3, a(n+3) = a(n) + a(n+1). 4
 1, 2, 3, 3, 5, 6, 8, 11, 14, 19, 25, 33, 44, 58, 77, 102, 135, 179, 237, 314, 416, 551, 730, 967, 1281, 1697, 2248, 2978, 3945, 5226, 6923, 9171, 12149, 16094, 21320, 28243, 37414, 49563, 65657, 86977, 115220, 152634, 202197, 267854, 354831 (list; graph; refs; listen; history; text; internal format)
 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 Sequence in context: A192184 A027586 A039860 * A300446 A039876 A239312 Adjacent sequences:  A084335 A084336 A084337 * A084339 A084340 A084341 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

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Last modified August 7 04:39 EDT 2020. Contains 336274 sequences. (Running on oeis4.)