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 A118451 Number of rooted n-edge maps on a non-orientable genus-3 surface. 2
 41, 1380, 31225, 592824, 10185056, 164037704, 2525186319, 37596421940, 545585129474, 7758174844664, 108518545261360, 1497384373878512, 20426386710028260, 275940187259609296, 3696482210884173349 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 REFERENCES 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. LINKS R. J. Mathar, Table of n, a(n) for n = 3..100 Didier Arquès, Alain Giorgetti, Counting rooted maps on a surface, Theoret. Comput. Sci. 234 (2000), no. 1-2, 255--272. MR1745078 (2001f:05078). - N. J. A. Sloane, Jul 27 2012 FORMULA O.g.f.: (R-1) *(R+1) *(68*R^5 +280*R^4 +588*R^3 +808*R^2 +416*R -(28*R^4+59*R^3+114*R^2+119*R+40)*sqrt(12*R*(R+2)))/ (96*R^5*(R+2)^3), where R=sqrt(1-12*x). MAPLE R := sqrt(1-12*x) ; (R-1)*(R+1)*(68*R^5+280*R^4+588*R^3+808*R^2+416*R -(28*R^4+59*R^3+114*R^2+119*R+40)*sqrt(12*R*(R+2)))/96/R^5/(R+2)^3 ; g := series(%, x=0, 101) ; for n from 3 to 100 do printf("%d %d\n", n, coeftayl(g, x=0, n)) ; end do: # R. J. Mathar, Oct 17 2012 MATHEMATICA R = Sqrt[1-12x]; (R-1)(R+1)(68R^5 + 280R^4 + 588R^3 + 808R^2 + 416R - (28R^4 + 59R^3 + 114R^2 + 119R + 40) Sqrt[12R(R+2)])/96/R^5/(R+2)^3 + O[x]^18 // CoefficientList[#, x]& // Drop[#, 3]& (* Jean-François Alcover, Aug 28 2019 *) CROSSREFS Cf. A006344, A214334. Sequence in context: A014937 A275225 A275145 * A094455 A239251 A197527 Adjacent sequences: A118448 A118449 A118450 * A118452 A118453 A118454 KEYWORD nonn AUTHOR Valery A. Liskovets, May 04 2006 STATUS approved

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Last modified December 8 23:09 EST 2023. Contains 367680 sequences. (Running on oeis4.)