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 A217067 Number of unlabeled graphs on n nodes whose components are cycles or complete graphs. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also number of partitions of n, with one kind of 1, 2 and 3 and two kinds of 4, 5, 6, ... . Number of n-vertex graphs that do not contain a triangle or claw as induced subgraph (there is one connected triangle-free claw-free graph with 1 to 3 vertices each, and two for n >= 4 vertices (P_n and C_n)). - Falk Hüffner, Jan 11 2016 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 N. J. A. Sloane, Transforms 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, ... . 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 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] PROG (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 CROSSREFS Cf. A000715. Sequence in context: A308995 A326470 A326595 * A014214 A094993 A192671 Adjacent sequences:  A217064 A217065 A217066 * A217068 A217069 A217070 KEYWORD nonn AUTHOR Geoffrey Critzer, Sep 26 2012 STATUS approved

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Last modified April 7 01:11 EDT 2020. Contains 333291 sequences. (Running on oeis4.)