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A118448
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Number of rooted n-edge one-vertex maps on a non-orientable genus-3 surface (dually: one-face maps).
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4
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41, 690, 7150, 58760, 420182, 2736524, 16661580, 96411060, 536075430, 2886649260, 15139322276, 77665981120, 391031449340, 1937266785080, 9464122525784, 45670084085004, 218002466412870, 1030588793671980
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OFFSET
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3,1
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COMMENTS
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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).
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REFERENCES
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E. R. Canfield, Calculating the number of rooted maps on a surface, Congr. Numerantium, 76 (1990), 21-34.
D. M. Jackson and T. I. Visentin, An atlas of the smaller maps in orientable and nonorientable surfaces. CRC Press, Boca Raton, 2001.
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LINKS
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FORMULA
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O.g.f.: (R-1)^3*(R+1)^2*(11*R^2-29*R-64)/(64*R^8), where R=sqrt(1-4*x).
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
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MATHEMATICA
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((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 *)
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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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