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Search: id:A126100
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| A126100 |
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Number of rooted connected unlabeled graphs on n nodes. |
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+0
3
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| 0, 1, 1, 3, 11, 58, 407, 4306, 72489, 2111013, 111172234, 10798144310, 1944301471861, 650202565436890, 404697467417019634, 470133531223369393920, 1022561022228933341815171, 4177761667636803276899047351, 32163582481439081597751699343141, 468019937132164016636736323752098741
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Let G run through all connected unlabeled graphs on n nodes. Add up the numbers of inequivalent nodes (under Aut(G)) for each G.
"Pointed" connected graphs. This has the same relation to A001349 as A000081 does to A000055.
a(0) = 0 because the empty graph cannot be rooted.
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LINKS
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David Applegate and N. J. A. Sloane, Table of n, a(n) for n = 0..23
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FORMULA
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The g.f. A(x) = x+x^2+3*x^3+11*x^4+... satisfies f(x) = 1 + A(x)*g(x), where f(x) = 1+x+2*x^2+6*x^3+20*x^4+... is the g.f. for A000666 and g(x) = 1+x+2*x^2+4*x^3+11*x^4+... is the g.f. for A000088. - Brendan McKay.
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EXAMPLE
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For 3 nodes G is either a path (2 kinds of nodes) or a triangle (one kind of node), for a total of a(3) = 3.
For the 5-vertex graphs we have 2 x 1 orbit, 6 x 2 orbits, 8 x 3 orbits, 5 x 4 orbits for a total of 2 + 12 + 24 + 20 = 58.
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CROSSREFS
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Cf. A001349, A126101, A000666, A000088, A126201.
Sequence in context: A001586 A126201 A020012 this_sequence A009444 A168325 A141776
Adjacent sequences: A126097 A126098 A126099 this_sequence A126101 A126102 A126103
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KEYWORD
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nonn,nice
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AUTHOR
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David Applegate (david(AT)research.att.com) and N. J. A. Sloane (njas(AT)research.att.com), Mar 05 2007
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EXTENSIONS
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a(5)-a(9) computed by Gordon Royle (gordon(AT)maths.uwa.edu.au), Mar 05 2007
a(10) and a(11) computed by Brendan McKay (bdm(AT)cs.anu.edu.au), Mar 05 2007
a(12) onwards computed from the generating function, A000088 and A000666 by D.A. and N. J. A. Sloane (njas(AT)research.att.com), Mar 06 2007
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