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Search: id:A069840
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| A069840 |
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Number of different (unlabeled) 2-cell embeddings of the n-wheel graph W_(n+1) on n+1 nodes into orientable surfaces. |
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+0
2
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| 16, 80, 666, 6588, 80886, 1146916, 18583160, 337808300, 6812539360, 150922350288, 3643698427650, 95221941543232, 2678117152113428, 80658585770586368, 2590036811212597862, 88333886984966359596
(list; graph; listen)
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OFFSET
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4,1
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COMMENT
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Values of a(n) for n <= 3 are not well-defined.
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REFERENCES
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B. P. Mull, R. G. Riepert and A. T. White, Enumerating 2-cell imbeddings of connected graphs. Proc. Amer. Math. Soc. 103 (1988), 321-330.
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FORMULA
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a(n)=1/(2*n)*sum_(d|n) phi(d)^2*2^(n/d)*(n/d-1)!*d^(n/d-1), n odd; a(n)=1/(2*n)*sum_(d|n) phi(d)^2*2^(n/d)*(n/d-1)!*d^(n/d-1)+ 2^(n-3)*(n/2-1)!, n even, where phi(n) is the Euler totient function A000010.
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MATHEMATICA
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f[n_] := Block[{d = Divisors[n], s}, s = Apply[Plus, EulerPhi[d]^2*2^(n/d)*(n/d - 1)!*d^(n/d - 1)]/(2n); If[ EvenQ[n], s = s + 2^(n - 3)*(n/2 - 1)! ]; s];
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CROSSREFS
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Cf. A069839.
Adjacent sequences: A069837 A069838 A069839 this_sequence A069841 A069842 A069843
Sequence in context: A050468 A068778 A034570 this_sequence A000817 A119508 A088379
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KEYWORD
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nonn
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AUTHOR
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Valery Liskovets (liskov(AT)im.bas-net.by), Apr 22 2002
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com) and Vladeta Jovovic (vladeta(AT)Eunet.yu), May 04 2002
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