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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.)