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Search: id:A007137
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| A007137 |
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Number of rooted maps with n edges on the projective plane.
(Formerly M4734)
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+0
2
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| 1, 10, 98, 982, 10062, 105024, 1112757, 11934910, 129307100, 1412855500, 15548498902, 172168201088, 1916619748084, 21436209373224, 240741065193282, 2713584138389838, 30687358107371442, 348061628432108352
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
E. A. Bender, E. R. Canfield and R. W. Robinson, The enumeration of maps on the torus and the projective plane, Canad. Math. Bull., 31 (1988), 257-271.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..100
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FORMULA
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G.f.: ((2*R+1)/3-sqrt(R*(R+2)/3))/(2*x) where R=sqrt(1-12*x); a(n) is asymptotic to sqrt(3/2)*12^n/(n^(5/4)*GAMMA(3/4)) - Pab Ter (pabrlos2(AT)yahoo.com), Nov 07 2005
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MAPLE
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R:=sqrt(1-12*x): seq(coeff(convert(series(((2*R+1)/3-sqrt(R*(R+2)/3))/(2*x), x, 50), polynom), x, n), n=1..25); (Pab Ter)
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CROSSREFS
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Cf. A006300.
Sequence in context: A125880 A125445 A163446 this_sequence A135927 A129542 A081109
Adjacent sequences: A007134 A007135 A007136 this_sequence A007138 A007139 A007140
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Reference gives 20 terms.
Description corrected May 15 1997 - thanks to Jean-Francois Beraud.
More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 07 2005
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