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A338999
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Number of connected multigraphs with n edges and rooted at two indistinguishable vertices whose removal leaves a connected graph.
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5
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1, 1, 3, 11, 43, 180, 804, 3763, 18331, 92330, 478795, 2547885, 13880832, 77284220, 439146427, 2543931619, 15010717722, 90154755356, 550817917537, 3421683388385, 21601986281226, 138548772267326, 902439162209914, 5967669851051612, 40053432076016812
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OFFSET
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1,3
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COMMENTS
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This sequence counts the CDE-descendants of a single edge A-Z.
[C]onnect: different nodes {P,Q} != {A,Z} may form a new edge P-Q.
[D]issect: any edge P-Q may be dissected into P-M-Q with a new node M.
[E]xtend: any node P not in {A,Z} may form a new edge P-Q with a new node Q.
These basic operations were motivated by A338487, which seemed to count the CDE-descendants of K_4 with edge A-Z removed.
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REFERENCES
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Technology Review's Puzzle Corner, How many different resistances can be obtained by combining 10 one ohm resistors? Oct 3, 2003.
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LINKS
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EXAMPLE
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The a(3) = 3 CDE-descendants of A-Z with 3 edges are
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A A A
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o o - o o - o
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Z Z Z
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DCC DD DE
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PROG
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InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v, n, polcoef(p, n)), vector(#v, n, 1/n))}
seq(n)={my(A=O(x*x^n), g=G(2*n, x+A, []), gr=G(2*n, x+A, [1])/g, u=InvEulerT(Vec(-1+G(2*n, x+A, [1, 1])/(g*gr^2))), t=InvEulerT(Vec(-1+G(2*n, x+A, [2])/(g*subst(gr, x, x^2)))), v=vector(n)); for(n=1, #v, v[n]=(u[n]+t[n]-if(n%2==0, u[n/2]-v[n/2]))/2); v} \\ Andrew Howroyd, Nov 20 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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