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%I #22 Aug 29 2019 05:27:53
%S 41,690,7150,58760,420182,2736524,16661580,96411060,536075430,
%T 2886649260,15139322276,77665981120,391031449340,1937266785080,
%U 9464122525784,45670084085004,218002466412870,1030588793671980
%N Number of rooted n-edge one-vertex maps on a non-orientable genus-3 surface (dually: one-face maps).
%C One-vertex maps on the Klein bottle are counted by A118447 and one-vertex maps on a non-orientable genus-4 surface by A118449. Such maps are also called bouquets of loops (and their duals are called unicellular maps).
%D E. R. Canfield, Calculating the number of rooted maps on a surface, Congr. Numerantium, 76 (1990), 21-34.
%D D. M. Jackson and T. I. Visentin, An atlas of the smaller maps in orientable and nonorientable surfaces. CRC Press, Boca Raton, 2001.
%H R. J. Mathar, <a href="/A118448/b118448.txt">Table of n, a(n) for n = 3..100</a>
%H Didier Arquès, Alain Giorgetti, <a href="https://doi.org/10.1016/S0304-3975(98)00230-8">Counting rooted maps on a surface</a>, Theoret. Comput. Sci. 234 (2000), no. 1-2, 255--272. MR1745078 (2001f:05078). - _N. J. A. Sloane_, Jul 27 2012
%F O.g.f.: (R-1)^3*(R+1)^2*(11*R^2-29*R-64)/(64*R^8), where R=sqrt(1-4*x).
%F Conjecture: (69104*n+95905)*(n-2)*(n-3) *a(n) +2*(n-3) *(34552*n^2-2691825*n+3948578) *a(n-1) +4*(-967456*n^3+10134720*n^2-23520179*n+15213000) *a(n-2) + 144 *(2*n-5) *(34552*n-41477) *(n-2) *a(n-3)=0. _R. J. Mathar_, Oct 17 2012
%t ((R-1)^3 (R+1)^2 (11 R^2 - 29 R - 64)/(64 R^8) /. R -> Sqrt[1-4x]) + O[x]^21 // CoefficientList[#, x]& // Drop[#, 3]& (* _Jean-François Alcover_, Aug 29 2019 *)
%Y A diagonal of A214337.
%K nonn
%O 3,1
%A _Valery A. Liskovets_, May 04 2006
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