A007307 a(n) = a(n-2) + a(n-3).

0, 1, 2, 1, 3, 3, 4, 6, 7, 10, 13, 17, 23, 30, 40, 53, 70, 93, 123, 163, 216, 286, 379, 502, 665, 881, 1167, 1546, 2048, 2713, 3594, 4761, 6307, 8355, 11068, 14662, 19423, 25730, 34085, 45153, 59815, 79238, 104968, 139053, 184206, 244021, 323259, 428227

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)

a(n) = (A000931(n+1) + A001608(n+1))/2. - Elmo R. Oliveira, Dec 31 2022

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
# second Maple program:
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

Cf. A000931, A001608.

Sequence in context: A032303 A032215 A117363 * A207617 A141576 A078019

Adjacent sequences: A007304 A007305 A007306 * A007308 A007309 A007310

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved