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A217201 Number of simple unlabeled graphs with n nodes of 2 colors whose components are cycles. 1
1, 0, 0, 4, 6, 8, 23, 42, 83, 166, 324, 622, 1236, 2366, 4595, 8900, 17225, 33212, 64376, 124360, 240819, 466284, 904149, 1753782, 3407225, 6623274, 12892131, 25116456, 48987833, 95633480, 186891367, 365549578, 715661254, 1402246154, 2749778317, 5396266284 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

EULER transform of 0,0,4,6,8,13,30,... A000029.

MAPLE

with (numtheory):

b:= n-> `if`(n<3, 0, add(phi(d)*2^(n/d)/(2*n), d=divisors(n))+

    `if`(irem(n, 2)=1, 2^((n-1)/2), 2^(n/2-1)+2^(n/2-2))):

a:= proc(n) option remember; local d, j; `if`(n=0, 1,

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

    end:

seq(a(n), n=0..40);  # Alois P. Heinz, Sep 27 2012

MATHEMATICA

Needs["Combinatorica`"]

a=Expand[Table[nn=n; CycleIndex[DihedralGroup[nn], s]/.Table[s[i]->2, {i, 1, nn}], {n, 1, 30}]];

nn=30; p=Product[1/(1- x^i)^a[[i]], {i, 3, nn}]; CoefficientList[Series[p, {x, 0, nn}], x]

(* Second program: *)

b[n_] := If[n < 3, 0, Sum[EulerPhi[d]*2^(n/d)/(2*n), {d, Divisors[n]}] +  If[Mod[n, 2] == 1, 2^((n - 1)/2), 2^(n/2 - 1) + 2^(n/2 - 2)]];

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*b[d], {d, Divisors[j]}]*a[n - j], {j, 1, n}]/n];

Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Nov 05 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A217194, A217093, A005380.

Sequence in context: A019196 A086561 A083790 * A074125 A063719 A272862

Adjacent sequences:  A217198 A217199 A217200 * A217202 A217203 A217204

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Sep 27 2012

STATUS

approved

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Last modified April 17 15:33 EDT 2021. Contains 343063 sequences. (Running on oeis4.)