A214337
Triangle read by rows: T(n,k) = number of rooted maps with n vertices and k faces on a non-orientable surface of type 3/2 (0 <= k <= n).
Original entry on oeis.org
0, 0, 41, 0, 690, 16925, 0, 7150, 237652, 4306778, 0, 58760, 2518957, 56864524, 910734615, 0, 420182, 22417804, 613687758, 11675167470, 174833737848
Offset: 0
Triangle begins:
0;
0, 41;
0, 690, 16925;
0, 7150, 237652, 4306778;
0, 58760, 2518957, 56864524, 910734615;
0, 420182, 22417804, 613687758, 11675167470, 174833737848;
...
A118449
Number of rooted n-edge one-vertex maps on a non-orientable genus-4 surface (dually: one-face maps).
Original entry on oeis.org
0, 488, 11660, 160680, 1678880, 14771680, 115457832, 827303280, 5545466520, 35257287120, 214730922120, 1262004908528, 7197437563680, 40007524376960, 217501266966160, 1159737346931040, 6079078540464072, 31385516059734960
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.
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With[{r=Sqrt[1-4x]},Drop[CoefficientList[Series[-(r-1)^4 (r+1)^3 (65r^3+ 337r^2- 433r-945)/(256r^11),{x,0,20}],x],3]] (* Harvey P. Dale, Aug 05 2019 *)
A118447
Number of rooted n-edge one-vertex maps on the Klein bottle (dually: one-face maps).
Original entry on oeis.org
4, 42, 304, 1870, 10488, 55412, 280768, 1379286, 6616360, 31144300, 144367584, 660746892, 2991902704, 13424189160, 59758420736, 264191654758, 1160934273288, 5074150057916, 22071747625120, 95596117130724
Offset: 2
- 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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((R - 1)^2 (R + 1) (R + 3)/(8 R^5) /. R -> Sqrt[1 - 4x]) + O[x]^22 // CoefficientList[#, x]& // Drop[#, 2]& (* Jean-François Alcover, Aug 28 2019 *)
Showing 1-3 of 3 results.
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