A217067 Number of unlabeled graphs on n nodes whose components are cycles or complete graphs.
1, 1, 2, 3, 6, 9, 15, 22, 35, 51, 77, 110, 162, 228, 326, 454, 637, 875, 1208, 1641, 2235, 3006, 4044, 5388, 7177, 9481, 12510, 16399, 21463, 27932, 36287, 46911, 60531, 77776, 99733, 127415, 162457, 206444, 261821, 331063, 417801, 525828, 660536, 827684
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..10000
- N. J. A. Sloane, Transforms
Crossrefs
Cf. A000715.
Programs
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Maple
a:= proc(n) a(n):= `if`(n=0, 1, add(add(d*`if`(d<4, 1, 2), d=numtheory[divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..50); # Alois P. Heinz, Sep 26 2012
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Mathematica
nn=40;a=x/(1-2x);p=Product[1/(1- x^i)^2,{i,1,nn}];CoefficientList[Series[p(1-x)(1-x^2)(1-x^3),{x,0,nn}],x] -
PARI
list(lim)=Vec((1-x)*(1-x^2)*(1-x^3)*prod(i=1, lim\=1, 1/(1-x^i)^2, O(x^lim++)+1)) \\ Charles R Greathouse IV, Sep 26 2012
Formula
G.f.: (1-x)(1-x^2)(1-x^3) Product_{i>=1} 1/(1-x^i)^2.
EULER transform of 1, 1, 1, 2, 2, 2, ... .
Comments