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 A096331 Number of 2-connected planar graphs on n labeled nodes. 9
 1, 10, 237, 10707, 774924, 78702536, 10273189176, 1631331753120, 304206135619160, 65030138045062272, 15659855107404275280, 4191800375194003211360, 1234179902360142341550240, 396280329098426228719121280, 137779269467538258010671193472 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 COMMENTS Recurrence known, see Bodirsky et al. REFERENCES Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p. 419. LINKS Gheorghe Coserea, Table of n, a(n) for n = 3..126 E. A. Bender, Z. Gao and N. C. Wormald, The number of labeled 2-connected planar graphs, Electron. J. Combin., 9 (2002), #R43. M. Bodirsky, C. Groepl and M. Kang, Generating Labeled Planar Graphs Uniformly At Random, ICALP03 Eindhoven, LNCS 2719, Springer Verlag (2003), 1095 - 1107. O. Gimenez and M. Noy, Asymptotic enumeration and limit laws of planar graphs, arXiv:math/0501269 [math.CO], 2005. FORMULA a(n) ~ g * n^(-7/2) * r^n * n!, where g=0.00000370445941594... (A291835) and r=26.1841125556... (A291836) (see Bender link). - Gheorghe Coserea, Sep 03 2017 PROG (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)))); }; A100960_ser(N) = { my(x='x+O('x^(3*N+1)), t='t+O('t^(N+4)), q=t*x*Ser(vector(3*N+1, n, Polrev(vector(min(N+3, 2*n\3), k, Q(n, k)), 't))), d=serreverse((1+x)/exp(q/(2*t^2*x) + t*x^2/(1+t*x))-1), g2=intformal(t^2/2*((1+d)/(1+x)-1))); serlaplace(Ser(vector(N, n, subst(polcoeff(g2, n, 't), 'x, 't)))*'x); }; Vec(subst(A100960_ser(20), 't, 1)) \\ Gheorghe Coserea, Aug 10 2017 CROSSREFS Cf. A066537. Row sums of A100960. Sequence in context: A188679 A167867 A268080 * A159497 A177595 A013922 Adjacent sequences: A096328 A096329 A096330 * A096332 A096333 A096334 KEYWORD nonn AUTHOR Steven Finch, Aug 02 2004 EXTENSIONS More terms from Gheorghe Coserea, Aug 05 2017 STATUS approved

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Last modified June 15 19:43 EDT 2024. Contains 373410 sequences. (Running on oeis4.)