|
%I M4022 N1669 #33 Mar 27 2021 23:02:35
%S 5,93,1030,8885,65954,442610,2762412,16322085,92400330,505403910,
%T 2687477780,13957496098,71053094420,355548314180,1752827693528,
%U 8529176056965,41026491589722,195327793313790,921451498774660,4311086414580022,20019238138410940
%N Number of genus 0 rooted planar maps with 4 faces and n vertices.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D T. R. S. Walsh, Combinatorial Enumeration of Non-Planar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.
%H T. D. Noe, <a href="/A000365/b000365.txt">Table of n, a(n) for n = 3..200</a>
%H W. T. Tutte, <a href="http://dx.doi.org/10.1090/S0002-9904-1968-11877-4">On the enumeration of planar maps</a>, Bull. Amer. Math. Soc. 74 1968 64-74.
%H T. R. S. Walsh and A. B. Lehman, <a href="http://dx.doi.org/10.1016/0095-8956(72)90056-1">Counting rooted maps by genus</a>, J. Comb. Thy B13 (1972), 122-141 and 192-218.
%H <a href="/A007401/a007401_1.pdf">Notes</a>
%F G.f.: x^2*(1-sqrt(1-4*x))*(7+4*x-2*sqrt(1-4*x))/(2*(4*x-1)^4). - corrected for right offset by _Vaclav Kotesovec_, Aug 13 2013
%F a(n) ~ n^3*4^n/24 * (1-4/(sqrt(Pi*n))). - _Vaclav Kotesovec_, Aug 13 2013
%t nn = 20; CoefficientList[Series[x^2 (1 - Sqrt[1 - 4 x]) (7 + 4 x - 2 Sqrt[1 - 4 x])/(2 (4 x - 1)^4), {x, 0, nn}], x] (* _T. D. Noe_, Jun 19 2012 *)
%o (PARI) seq(n)={my(g=sqrt(1-4*x + O(x*x^n))); Vec((1-g)*(7+4*x-2*g)/(2*(1-4*x)^4))} \\ _Andrew Howroyd_, Mar 27 2021
%Y Column 4 of A269920.
%Y Column 0 of A270408.
%K nonn
%O 3,1
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Nov 14 2010
|
