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Search: id:A000939
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| A000939 |
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Number of inequivalent n-gons.
(Formerly M1280 N0491)
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+0
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; listen)
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OFFSET
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3,2
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COMMENT
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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
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S. W. Golomb and L. R. Welch, On the enumeration of polygons, Amer. Math. Monthly, 67 (1960), 349-353.
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LINKS
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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
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For formula see Maple lines.
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MAPLE
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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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CROSSREFS
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Cf. A000940. Bisections give A094154, A094155.
Adjacent sequences: A000936 A000937 A000938 this_sequence A000940 A000941 A000942
Sequence in context: A006385 A131180 A047990 this_sequence A109154 A030853 A030962
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KEYWORD
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nonn,nice,easy
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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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