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Search: id:A000940
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| A000940 |
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Number of n-gons.
(Formerly M1260 N0482)
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+0
5
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| 1, 2, 4, 12, 39, 202, 1219, 9468, 83435, 836017, 9223092, 111255228, 1453132944, 20433309147, 307690667072, 4940118795869, 84241805734539, 1520564059349452, 28963120073957838, 580578894859915650, 12217399235411398127, 269291841184184374868, 6204484017822892034404
(list; graph; listen)
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OFFSET
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3,2
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COMMENT
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Number of inequivalent undirected Hamiltonian cycles in complete graph on n labeled nodes under action of dihedral group of order 2n acting on nodes.
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REFERENCES
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S. W. Golomb and L. R. Welch, On the enumeration of polygons, Amer. Math. Monthly, 67 (1960), 349-353.
E. M. Palmer and R. W. Robinson, Enumeration under two representations of the wreath product, Acta Math., 131 (1973), 123-143.
R. C. Read, Combinatorial problems in theory of music, Discrete Math. 167 (1997), 543-551.
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LINKS
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T. D. Noe, Table of n, a(n) for n=3..100
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FORMULA
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For formula see Maple lines.
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MAPLE
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with(numtheory); # for n odd: Sd:=proc(n) local t1, d; t1:=2^((n-1)/2)*n^2*((n-1)/2)!; for d from 1 to n do if n mod d = 0 then t1:=t1+phi(n/d)^2*d!*(n/d)^d; fi; od: t1/(4*n^2); end;
# for n even: Se:=proc(n) local t1, d; t1:=2^(n/2)*n*(n+6)*(n/2)!/4; for d from 1 to n do if n mod d = 0 then t1:=t1+phi(n/d)^2*d!*(n/d)^d; fi; od: t1/(4*n^2); end; A000940:=n-> if n mod 2 = 0 then Se(n) else Sd(n); fi;
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CROSSREFS
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Cf. A000939. Bisections give A094156, A094157.
Adjacent sequences: A000937 A000938 A000939 this_sequence A000941 A000942 A000943
Sequence in context: A003701 A114500 A108532 this_sequence A008404 A099214 A126946
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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More terms from Pab Ter (pabrlos(AT)yahoo.com), May 05 2004
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