login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A215981 Number of simple unlabeled graphs on n nodes with exactly 1 connected component that is a tree or a cycle. 4
1, 1, 2, 3, 4, 7, 12, 24, 48, 107, 236, 552, 1302, 3160, 7742, 19321, 48630, 123868, 317956, 823066, 2144506, 5623757, 14828075, 39299898, 104636891, 279793451, 751065461, 2023443033, 5469566586, 14830871803, 40330829031, 109972410222, 300628862481 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..700

FORMULA

a(1) = a(2) = 1, a(n) = 1 + A000055(n) for n>=3.

EXAMPLE

a(5) = 4: .o-o-o.  .o-o-o.  .o-o-o.  .o-o-o.

          .|  / .  .|    .  .| |  .  . /|  .

          .o-o  .  .o-o  .  .o o  .  .o o  .

MAPLE

with(numtheory):

b:= proc(n) option remember; local d, j; `if`(n<=1, n,

      (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/(n-1))

    end:

a:= proc(n) option remember; local k; `if`(n>2, 1, 0)+ b(n)-

      (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2

    end:

seq(a(n), n=1..40);

MATHEMATICA

b[n_] := b[n] = If[n <= 1, n, (Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n - j], {j, 1, n - 1}])/(n - 1)];

a[n_] := a[n] = If[n > 2, 1, 0] + b[n] - (Sum[b[k]*b[n - k], {k, 0, n}] - If[Mod[n, 2] == 0, b[n/2], 0])/2;

Array[a, 40] (* Jean-Fran├žois Alcover, Mar 21 2017, translated from Maple *)

CROSSREFS

Column k=1 of A215977.

The labeled version is A215851.

Cf. A000055, A215978.

Sequence in context: A006706 A194079 A124390 * A107031 A207573 A152605

Adjacent sequences:  A215978 A215979 A215980 * A215982 A215983 A215984

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 29 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 19:26 EDT 2021. Contains 348215 sequences. (Running on oeis4.)