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A096330
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Number of 3-connected planar graphs on n labeled nodes.
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3
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1, 25, 1227, 84672, 7635120, 850626360, 112876089480, 17381709797760, 3046480841900160, 598731545755324800, 130389773403373545600, 31163616486434838067200, 8109213009296586130944000, 2282014010657773764160588800, 690521215428258768326957184000
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OFFSET
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4,2
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COMMENTS
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Recurrence known, see Bodirsky et al.
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REFERENCES
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M. Bodirsky, C. Groepl and M. Kang: Generating Labeled Planar Graphs Uniformly At Random; ICALP03 Eindhoven, LNCS 2719, Springer Verlag (2003), 1095 - 1107.
Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p. 419.
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LINKS
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PROG
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(PARI)
Q(n, k) = { \\ c-nets with n-edges, k-vertices
if (k < 2+(n+2)\3 || k > 2*n\3, return(0));
sum(i=2, k, sum(j=k, n, (-1)^((i+j+1-k)%2)*binomial(i+j-k, i)*i*(i-1)/2*
(binomial(2*n-2*k+2, k-i)*binomial(2*k-2, n-j) -
4*binomial(2*n-2*k+1, k-i-1)*binomial(2*k-3, n-j-1))));
};
a(n) = sum(k=(3*n+1)\2, 3*n-6, n!*Q(k, n)/(4*k));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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