A165648 Number of disconnected simple graphs on n vertices with each component regular.

0, 1, 2, 4, 7, 13, 23, 41, 77, 149, 397, 1246, 21135, 430933, 51156773, 3044120326, 1704554902881, 446193132548644, 650868899188542416, 431014163502227412545, 2886915606822315071638459, 8841362446647790021087061250, 152946959203764346079534774815394, 1208238394473886999896406262410758886

Offset

1,3

Links

Table of n, a(n) for n=1..24.

Formula

a(n) = A165647(n) - A005177(n)

= Euler_transformation(A005177)(n) - A005177(n).

Example

The a(2)=1 graph is: 2K_1. The a(3)=2 graphs are: 3K_1, K_1+K_2. The a(4)=4 graphs are: 4K_1, 2K_1+K_2, K_1+K_3, 2K_2.

Mathematica

A005177 = Cases[Import["https://oeis.org/A005177/b005177.txt", "Table"], {_, _}][[All, 2]]~Join~{0};
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[DivisorSum[j, # p[#]&] b[n - j], {j, 1, n}]/n]; b];
b = etr[A005177[[# + 1]]&];
a[n_] := b[n] - A005177[[n + 1]];
a /@ Range[17] (* Jean-François Alcover, Dec 02 2019 *)

Crossrefs

Cf. A005177, A165647.

Sequence in context: A368299 A303666 A260917 * A287381 A078038 A190502

Adjacent sequences: A165645 A165646 A165647 * A165649 A165650 A165651

Keyword

nonn,hard

Author

Jason Kimberley, Sep 23 2009

Extensions

Terms a(18) and beyond from Andrew Howroyd, May 21 2020

Status

approved