login
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
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
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
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: A027586 A339405 A039860 * A300446 A039876 A239312
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