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A060576
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a(n) = 1 except for a(1) = 0.
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21
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1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list;
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refs;
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history;
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internal format)
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OFFSET
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0,1
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COMMENTS
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Old name: Number of homeomorphically irreducible general graphs on 1 labeled node and with n edges.
A homeomorphically irreducible general graph is a graph with multiple edges and loops and without nodes of degree 2.
This sequence is also produced by Wolfram's Rule 253 of Elementary Cellular Automaton as a triangle read by rows giving successive states initiated with a single ON (black) cell. See the Wolfram, Weisstein and Index links below. - Robert Price, Jan 31 2016
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.
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LINKS
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FORMULA
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G.f.: (x^2 - x + 1)/(1 - x). a(0)=1, a(1)=0; a(n)=1, n > 1.
E.g.f. for homeomorphically irreducible general graphs with n nodes and k edges is (1 + x*y)^(- 1/2)*exp(- x*y/2 + x^2*y^2/4)*Sum_{k >= 0} 1/(1 - x)^binomial(k + 1, 2)*exp(- x^2*y*k^2/(2*(1 + x*y)) - x^2*y*k/2)*y^k/k!.
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MAPLE
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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