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Search: id:A118447
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| A118447 |
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Number of rooted n-edge one-vertex maps on the Klein bottle (dually: one-face maps). |
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+0
2
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| 4, 42, 304, 1870, 10488, 55412, 280768, 1379286, 6616360, 31144300, 144367584, 660746892, 2991902704, 13424189160, 59758420736, 264191654758, 1160934273288, 5074150057916, 22071747625120, 95596117130724
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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One-vertex maps on the projective plane are counted by A000346, and one-vertex maps on a non-orintable genus-3 surface by A118448. 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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FORMULA
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O.g.f.: (R-1)^2(R+1)(R+3)/8R^5, where R=sqrt(1-4x).
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CROSSREFS
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Sequence in context: A076652 A078288 A089551 this_sequence A037296 A085954 A046719
Adjacent sequences: A118444 A118445 A118446 this_sequence A118448 A118449 A118450
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KEYWORD
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nonn
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AUTHOR
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Valery A. Liskovets (liskov(AT)im.bas-net.by), May 04 2006
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