The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A215981

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A215981

Number of simple unlabeled graphs on n nodes with exactly 1 connected component that is a tree or a cycle.
(history; published version)

#16 by R. J. Mathar at Sat Jun 16 12:51:19 EDT 2018

STATUS

editing

approved

#15 by R. J. Mathar at Sat Jun 16 12:51:08 EDT 2018

CROSSREFS

Cf. A000055, A215978.

STATUS

approved

editing

#14 by Bruno Berselli at Tue Mar 21 13:08:41 EDT 2017

STATUS

proposed

approved

#13 by Jean-François Alcover at Tue Mar 21 12:31:34 EDT 2017

STATUS

editing

proposed

#12 by Jean-François Alcover at Tue Mar 21 12:31:29 EDT 2017

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-François Alcover, Mar 21 2017, translated from Maple *)

STATUS

approved

editing

#11 by Alois P. Heinz at Thu Dec 04 06:49:49 EST 2014

STATUS

editing

approved

#10 by Alois P. Heinz at Thu Dec 04 06:49:40 EST 2014

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))

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

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

STATUS

approved

editing

#9 by Alois P. Heinz at Wed Aug 29 23:07:45 EDT 2012

STATUS

editing

approved

#8 by Alois P. Heinz at Wed Aug 29 18:04:54 EDT 2012

EXAMPLE

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

#7 by Alois P. Heinz at Wed Aug 29 18:01:44 EDT 2012

CROSSREFS

The labeled version is A215851.