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Search: id:A001004
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| A001004 |
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Number of symmetric dissections of a polygon.
(Formerly M0898 N0339)
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+0
4
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| 1, 1, 2, 3, 9, 20, 75, 262, 1117, 4783, 21971, 102249, 489077, 2370142, 11654465, 57916324, 290693391, 1471341341, 7504177738, 38532692207, 199076194985, 1034236705992, 5400337050086, 28329240333758, 149244907249629
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also number of 2-connected outerplanar graphs on n unlabeled nodes. - S. R. Finch (Steven.Finch(AT)inria.fr), Dec 09 2004
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REFERENCES
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Guanzhang Hu, Group theory method for enumeration of outerplanar graphs, Acta Math. Appl. Sinica 14 (1998) 381-387.
P. Lisonek, Closed forms for the number of polygon dissections. Journal of Symbolic Computation 20 (1995), 595-601.
T. S. Motzkin, Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products, Bull. Amer. Math. Soc., 54 (1948), 352-360.
R. C. Read, On general dissections of a polygon, Aequat. Math. 18 (1978), 370-388.
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LINKS
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S. R. Finch, Planar graph growth constants.
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MATHEMATICA
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f[x_, n_]:=x+Sum[(1/r)*Binomial[s-2, r-1]*Binomial[r+s-1, s]*x^s, {r, 1, n}, {s, 2, n}]; F[x_, n_]:=Series[((3x^2-2*x*f[x, n]+f[x, n]^2)- (2+2*x+7*x^2-4*x*f[x, n]+2*f[x, n]^2)*f[x^2, n]+ 2*f[x^2, n]^2)/(4*(2*f[x^2, n]-1))+Sum[If[Mod[k, d]==0, EulerPhi[d]*f[x^d, n]^(k/d)/k, 0], {k, 3, n}, {d, 1, k}]/2, {x, 0, n}]; F[x, 22] (Finch)
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CROSSREFS
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Adjacent sequences: A001001 A001002 A001003 this_sequence A001005 A001006 A001007
Sequence in context: A097075 A036673 A111189 this_sequence A015951 A101531 A099607
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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 Esa Peuha (esa.peuha(AT)helsinki.fi), Oct 21 2005
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