A084338 a(1) = 1, a(2) = 2, a(3) = 3, a(n+3) = a(n) + a(n+1).

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

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 18 2003

Keywords

• nonn
• easy

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).

Programs

Haskell

a084338_list = [1,2,3] ++ zipWith (+) a084338_list (tail a084338_list)
a084338 n = a084338_list !! (n - 1)
-- Jack Willis, Dec 22 2013

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 *)

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)

Extensions

More terms from Erich Friedman, Aug 08 2005