A267180
Triangle read by rows: T(n,k) = number of rooted maps with n edges on a nonorientable surface of genus k (1 <= k <= n).
Original entry on oeis.org
1, 10, 4, 98, 84, 41, 982, 1340, 1380, 488, 10062, 19280, 31225, 23320, 8229, 105024, 263284, 592824, 696912, 516958, 164892, 1112757, 3486224, 10185056, 16662492, 19381145, 12980716, 4016613, 11934910, 45247084, 164037704, 348539072, 562395292, 590136856, 382630152, 112818960
Offset: 1
Triangle begins:
1,
10,4,
98,84,41,
982,1340,1380,488,
10062,19280,31225,23320,8229,
105024,263284,592824,696912,516958,164892,
1112757,3486224,10185056,16662492,19381145,12980716,4016613,
11934910,45247084,164037704,348539072,562395292,590136856,382630152,112818960
...
- David M. Jackson and Terry I. Visentin, An Atlas of the Smaller Maps in Orientable and Nonorientable Surfaces, Chapman & Hall/CRC, circa 2000. See page 227.
See
A238396 for analog for orientable surfaces.
A118451
Number of rooted n-edge maps on a non-orientable genus-3 surface.
Original entry on oeis.org
41, 1380, 31225, 592824, 10185056, 164037704, 2525186319, 37596421940, 545585129474, 7758174844664, 108518545261360, 1497384373878512, 20426386710028260, 275940187259609296, 3696482210884173349
Offset: 3
- 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.
-
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
-
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 *)
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