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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A058860 Number of 2-connected rooted cubic planar maps with n faces.

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%I A058860 #22 Jul 22 2018 21:56:12
%S A058860 1,3,19,128,909,6737,51683,407802,3293497,27122967,227095683,
%T A058860 1928656876,16582719509,144125955717,1264625068163,11190598332502,
%U A058860 99776445196977,895685185070155,8090065969366259,73480719648381240,670821169614526749
%N A058860 Number of 2-connected rooted cubic planar maps with n faces.
%H A058860 Gheorghe Coserea, <a href="/A058860/b058860.txt">Table of n, a(n) for n = 4..306</a>
%H A058860 Z. Gao and N. C. Wormald, <a href="http://users.monash.edu.au/~nwormald/papers/cubicplanar.ps.gz">Enumeration of rooted cubic planar maps</a>
%H A058860 Z. Gao and N. C. Wormald, <a href="https://doi.org/10.1007/s000260200006">Enumeration of rooted cubic planar maps</a>, Annals of Combinatorics, 6 (2002), no. 3-4, 313-325.
%F A058860 G.f.: x^2*(f-x)*(1-2*x)/(1+x), where f is defined by 16*x^2*f^3 + (8*x^4+24*x^3+72*x^2+8*x)*f^2 + (x^6+6*x^5-5*x^4-40*x^3+3*x^2-14*x+1)*f - x^4-3*x^3+13*x^2-x=0. - _Emeric Deutsch_, Nov 30 2005
%F A058860 From _Gheorghe Coserea_, Jul 14 2018: (Start)
%F A058860 G.f. y=A(x) satisfies:
%F A058860 0 = 16*y^3 - 8*x*(2*x - 1)*(x^2 + 8*x + 1)*y^2 + x^2*(2*x - 1)^2*(x^4 + 20*x^3 + 50*x^2 - 16*x + 1)*y - x^6*(2*x - 1)^3*(x^2 + 11*x - 1).
%F A058860 0 = x^3*(2*x - 1)^3*(x - 2)*(4*x - 5)*(2*x^2 + 10*x - 1)*y''' - x^2*(2*x - 1)^2*(96*x^5 + 188*x^4 - 1570*x^3 + 1791*x^2 - 481*x + 35)*y'' + 12*x*(2*x - 1)*(48*x^6 + 104*x^5 - 898*x^4 + 1186*x^3 - 514*x^2 + 95*x - 5)*y' - 6*(256*x^7 + 608*x^6 - 5456*x^5 + 8292*x^4 - 4962*x^3 + 1525*x^2 - 220*x + 10)*y.
%F A058860 (End)
%e A058860 G.f. = x^4 + 3*x^5 + 19*x^6 + 128*x^7 + 909*x^8 + 6737*x^9 + 51683*x^10 + ... - _Michael Somos_, Jul 22 2018
%p A058860 eq:=16*x^2*f^3+(8*x^4+24*x^3+72*x^2+8*x)*f^2+(x^6+6*x^5-5*x^4-40*x^3+3*x^2-14*x+1)*f-x^4-3*x^3+13*x^2-x: f:=sum(A[j]*x^j,j=1..35): for n from 1 to 35 do A[n]:=solve(coeff(expand(eq),x^n)=0) od: C2:=x^2*(f-x)*(1-2*x)/(1+x): C2ser:=series(C2,x=0,30): seq(coeff(C2ser,x^n),n=4..26); # _Emeric Deutsch_, Nov 30 2005
%o A058860 (PARI)
%o A058860 F = x^2*(z - x)*(1 - 2*x)/(1 + x);
%o A058860 G = 16*x^4*z^3 + x*(8*x^4 + 24*x^3 + 72*x^2 + 8*x)*z^2 + (x^6 + 6*x^5 -5*x^4 -40*x^3 + 3*x^2 - 14*x + 1)*z - x^3 - 3*x^2 + 13*x - 1;
%o A058860 Z(N) = {
%o A058860   my(z0 = 1 + O('x^N), z1=0, n=1);
%o A058860   while (n++,
%o A058860     z1 = z0 - subst(G, 'z, z0)/subst(deriv(G, 'z), 'z, z0);
%o A058860     if (z1 == z0, break()); z0 = z1); z0;
%o A058860 };
%o A058860 seq(N) = Vec(subst(F, 'z, 'x*Z(N+1)));
%o A058860 seq(21)
%o A058860 \\ test: y=Ser(seq(303),'x)*x^4; 0 == 16*y^3 - 8*x*(2*x - 1)*(x^2 + 8*x + 1)*y^2 + x^2*(2*x - 1)^2*(x^4 + 20*x^3 + 50*x^2 - 16*x + 1)*y - x^6*(2*x - 1)^3*(x^2 + 11*x - 1)
%o A058860 \\ _Gheorghe Coserea_, Jul 14 2018
%Y A058860 Cf. A000260, A058859, A058861.
%K A058860 nonn
%O A058860 4,2
%A A058860 _N. J. A. Sloane_, Jan 06 2001; revised Feb 17 2006
%E A058860 More terms from _Emeric Deutsch_, Nov 30 2005