

A060576


Number of homeomorphically irreducible general graphs on 1 labeled node and with n edges.


20



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
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OFFSET

0,1


COMMENTS

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


REFERENCES

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.


LINKS

Table of n, a(n) for n=0..104.
V. Jovovic, Generating functions for homeomorphically irreducible general graphs on n labeled nodes
V. Jovovic, Recurrences for the numbers of homeomorphically irreducible general graphs on m labeled nodes and n edges
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
Index to Elementary Cellular Automata
Index entries for sequences related to cellular automata
Index entries for linear recurrences with constant coefficients, signature (1).


FORMULA

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!.
E.g.f.: e^xx.  Paul Barry, May 06 2007
a(n) = 1  C(1,n) + C(0,n), with n>=0.  Paolo P. Lava, Feb 15 2008
a(n) = 1  binomial(0,n1).  Arkadiusz Wesolowski, Feb 10 2012


MAPLE

1, 0, seq(1, n=2..200); # Wesley Ivan Hurt, Apr 12 2017


PROG

(PARI) a(n)=n!=1 \\ Charles R Greathouse IV, Jun 06 2013


CROSSREFS

Cf. A003514, A060516, A060533A060537, A060577A060581.
Sequence in context: A324113 A105812 A134323 * A261012 A019590 A154955
Adjacent sequences: A060573 A060574 A060575 * A060577 A060578 A060579


KEYWORD

nonn,easy


AUTHOR

Vladeta Jovovic, Apr 03 2001


STATUS

approved



