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 A291371 Number of maximal chord diagrams of genus g counted up to rotations and reflections. 1
 1, 4, 82, 7258, 1491629, 506855279, 254118439668, 176377605783906, 162019808170348933, 190375587419231088550, 278587959330563466969926, 496903413656110608290219603 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also the number of non-isomorphic one-face one-vertex maps on a genus g surface where both orientation-preserving and orientation-reversing isomorphisms are taken into account. LINKS Evgeniy Krasko, Counting Unlabelled Chord Diagrams of Maximal Genus, arXiv:1709.00796 [math.CO], 2017. Evgeny Krasko, A. Omelchenko, Enumeration of Chord Diagrams without Loops and Parallel Chords, arXiv preprint arXiv:1601.05073 [math.CO], 2016; Electronic Journal of Combinatorics 24(3) (2017), #P3.43 PROG (Python 2.7) rot_sym = [   0, 1, 4, 131, 14118, 2976853, 1013582110, 508233789579, 352755124921122,   324039613564554401, 380751174738424280720, 557175918657122229139987,   993806827312044893602464496, # A291172 ] def u(n):   if n < 0:     return 0   if n <= 1:     return 1   sum = 0   sum -= (4 * n - 1) * u(n - 1)   sum += n * (2 * n - 3) * (10 * n - 9) * u(n - 2)   sum += 5 * (2 * n - 3) * (2 * n - 4) * (2 * n - 5) * u(n - 3)   sum -= 2 * (2 * n - 3) * (2 * n - 4) * (2 * n - 5) * (2 * n - 6) * (2 * n - 7) * u(n - 4)   return sum / (n + 1) for i in range(1, 13):   print (2 * rot_sym[i] + u(i) + u(i - 1) * (2 * i - 1)) / 4 CROSSREFS Maximal diagrams up to rotations: A291172. Sequence in context: A289224 A158981 A317889 * A007154 A056410 A056400 Adjacent sequences:  A291368 A291369 A291370 * A291372 A291373 A291374 KEYWORD nonn AUTHOR Evgeniy Krasko, Sep 03 2017 STATUS approved

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Last modified August 4 19:54 EDT 2020. Contains 336202 sequences. (Running on oeis4.)