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A000939
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Number of inequivalent n-gons.
(Formerly M1280 N0491)
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4
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1, 2, 4, 14, 54, 332, 2246, 18264, 164950, 1664354, 18423144, 222406776, 2905943328, 40865005494, 615376173184, 9880209206458, 168483518571798, 3041127561315224, 57926238289970076, 1161157777643184900, 24434798429947993054, 538583682082245127336
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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COMMENTS
| Here two n-gons are said to be equivalent if the differ in starting point, orientation, or a rotation (but not by a reflection - for that see A000940>
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REFERENCES
| S. W. Golomb and L. R. Welch, On the enumeration of polygons, Amer. Math. Monthly, 67 (1960), 349-353.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=3..100
A. Stoimenow, Enumeration of chord diagrams and an upper bound for Vassiliev invariants, J. Knot Theory Ramifications, 7 (1998), no. 1, 93-114.
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FORMULA
| For formula see Maple lines.
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MAPLE
| with(numtheory); # for n odd: Ed:=proc(n) local t1, d; t1:=0; 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/(2*n^2); end;
# for n even: Ee:=proc(n) local t1, d; t1:=2^(n/2)*(n/2)*(n/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/(2*n^2); end; A000939:=n-> if n mod 2 = 0 then Ee(n) else Ed(n); fi;
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MATHEMATICA
| a[n_] := (t = If[OddQ[n], 0, 2^(n/2)*(n/2)*(n/2)!];
Do[If[Mod[n, d]==0 , t = t+EulerPhi[n/d]^2*d!*(n/d)^d], {d, 1, n}]; t/(2*n^2)); a /@ Range[3, 24]
(* From Jean-François Alcover, May 19 2011, after Maple prog. *)
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CROSSREFS
| Cf. A000940. Bisections give A094154, A094155.
Sequence in context: A183949 A131180 A047990 * A109154 A030853 A030962
Adjacent sequences: A000936 A000937 A000938 * A000940 A000941 A000942
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Pab Ter (pabrlos(AT)yahoo.com), May 05 2004
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