OFFSET
0,3
COMMENTS
Also the number of maximal matchings in the (n-2)-pan graph. - Eric W. Weisstein, Dec 30 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Maximal Independent Edge Set
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-2) = p(n+1) + p(n-2), with p(n):=A000931(n+3).
O.g.f: x*(1+2*x)/(1-x^2-x^3). (End)
MAPLE
G(x):=(-1-x^3)/(-1+x^2+x^3): f[0]:=G(x): for n from 1 to 58 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n]/n!, n=1..43); # Zerinvary Lajos, Mar 27 2009
# Alternative:
a:= n-> (<<0|1|0>, <0|0|1>, <1|1|0>>^n.<<($0..2)>>)[1$2]:
seq(a(n), n=0..60); # Alois P. Heinz, Nov 06 2016
MATHEMATICA
Table[- RootSum[-1 - # + #^3 &, -16 #^n - 13 #^(n + 1) + #^(n + 2) &]/23, {n, 20}] (* Eric W. Weisstein, Dec 30 2017 *)
LinearRecurrence[{0, 1, 1}, {1, 3, 3}, 20] (* Eric W. Weisstein, Dec 30 2017 *)
CoefficientList[Series[x (-1 - 3 x - 2 x^2)/(-1 + x^2 + x^3), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 30 2017 *)
PROG
(Magma) I:=[0, 1, 2]; [n le 3 select I[n] else Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jun 09 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved
